diff --git a/.changeset/neat-carrots-guess.md b/.changeset/neat-carrots-guess.md
new file mode 100644
index 0000000000..375bbbed7b
--- /dev/null
+++ b/.changeset/neat-carrots-guess.md
@@ -0,0 +1,6 @@
+---
+"@khanacademy/perseus": minor
+"@khanacademy/perseus-editor": minor
+---
+
+[Interactive Graph Editor] Add the ability to reorder locked figure settings
diff --git a/packages/perseus-editor/src/components/__stories__/locked-ellipse-settings.stories.tsx b/packages/perseus-editor/src/components/__stories__/locked-ellipse-settings.stories.tsx
index 7945f9313e..ade3409a31 100644
--- a/packages/perseus-editor/src/components/__stories__/locked-ellipse-settings.stories.tsx
+++ b/packages/perseus-editor/src/components/__stories__/locked-ellipse-settings.stories.tsx
@@ -14,21 +14,21 @@ export const Default = (args): React.ReactElement => {
     return <LockedEllipseSettings {...args} />;
 };
 
-type StoryComponentType = StoryObj<typeof LockedEllipseSettings>;
-
-// Set the default values in the control panel.
-Default.args = {
+const defaultProps = {
     ...getDefaultFigureForType("ellipse"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
+type StoryComponentType = StoryObj<typeof LockedEllipseSettings>;
+
+// Set the default values in the control panel.
+Default.args = defaultProps;
+
 export const Controlled: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("ellipse"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -57,10 +57,7 @@ Controlled.parameters = {
 export const Expanded: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("ellipse"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
diff --git a/packages/perseus-editor/src/components/__stories__/locked-line-settings.stories.tsx b/packages/perseus-editor/src/components/__stories__/locked-line-settings.stories.tsx
index 8c053f8158..50c762d67a 100644
--- a/packages/perseus-editor/src/components/__stories__/locked-line-settings.stories.tsx
+++ b/packages/perseus-editor/src/components/__stories__/locked-line-settings.stories.tsx
@@ -14,21 +14,21 @@ export const Default = (args): React.ReactElement => {
     return <LockedLineSettings {...args} />;
 };
 
-type StoryComponentType = StoryObj<typeof LockedLineSettings>;
-
-// Set the default values in the control panel.
-Default.args = {
+const defaultProps = {
     ...getDefaultFigureForType("line"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
+type StoryComponentType = StoryObj<typeof LockedLineSettings>;
+
+// Set the default values in the control panel.
+Default.args = defaultProps;
+
 export const Controlled: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("line"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -57,10 +57,7 @@ Controlled.parameters = {
  */
 export const WithInvalidPoints: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("line"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -87,10 +84,7 @@ export const WithInvalidPoints: StoryComponentType = {
 export const Expanded: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("line"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -115,8 +109,7 @@ export const ExpandedNondefaultProps: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
         const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("line"),
-            onRemove: () => {},
+            ...defaultProps,
             kind: "segment" as const,
             color: "green" as const,
             lineStyle: "dashed" as const,
diff --git a/packages/perseus-editor/src/components/__stories__/locked-point-settings.stories.tsx b/packages/perseus-editor/src/components/__stories__/locked-point-settings.stories.tsx
index a500d36bb6..1b45eeff3f 100644
--- a/packages/perseus-editor/src/components/__stories__/locked-point-settings.stories.tsx
+++ b/packages/perseus-editor/src/components/__stories__/locked-point-settings.stories.tsx
@@ -14,21 +14,21 @@ export const Default = (args): React.ReactElement => {
     return <LockedPointSettings {...args} />;
 };
 
-type StoryComponentType = StoryObj<typeof LockedPointSettings>;
-
-// Set the default values in the control panel.
-Default.args = {
+const defaultProps = {
     ...getDefaultFigureForType("point"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
+type StoryComponentType = StoryObj<typeof LockedPointSettings>;
+
+// Set the default values in the control panel.
+Default.args = defaultProps;
+
 export const Controlled: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("point"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -54,10 +54,7 @@ Controlled.parameters = {
 export const Expanded: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("point"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -81,12 +78,7 @@ export const Expanded: StoryComponentType = {
 export const ExpandedNondefaultProps: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("point"),
-            onRemove: () => {},
-            color: "green" as const,
-            filled: false,
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
diff --git a/packages/perseus-editor/src/components/__stories__/locked-polygon-settings.stories.tsx b/packages/perseus-editor/src/components/__stories__/locked-polygon-settings.stories.tsx
index 45a6116950..b0836aae80 100644
--- a/packages/perseus-editor/src/components/__stories__/locked-polygon-settings.stories.tsx
+++ b/packages/perseus-editor/src/components/__stories__/locked-polygon-settings.stories.tsx
@@ -14,21 +14,21 @@ export const Default = (args): React.ReactElement => {
     return <LockedPolygonSettings {...args} />;
 };
 
-type StoryComponentType = StoryObj<typeof LockedPolygonSettings>;
-
-// Set the default values in the control panel.
-Default.args = {
+const defaultProps = {
     ...getDefaultFigureForType("polygon"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
+type StoryComponentType = StoryObj<typeof LockedPolygonSettings>;
+
+// Set the default values in the control panel.
+Default.args = defaultProps;
+
 export const Controlled: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("polygon"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -57,10 +57,7 @@ Controlled.parameters = {
 export const Expanded: StoryComponentType = {
     render: function Render() {
         const [expanded, setExpanded] = React.useState(true);
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("polygon"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
diff --git a/packages/perseus-editor/src/components/__stories__/locked-vector-settings.stories.tsx b/packages/perseus-editor/src/components/__stories__/locked-vector-settings.stories.tsx
index d2f765b2a2..4886bf5311 100644
--- a/packages/perseus-editor/src/components/__stories__/locked-vector-settings.stories.tsx
+++ b/packages/perseus-editor/src/components/__stories__/locked-vector-settings.stories.tsx
@@ -14,21 +14,21 @@ export const Default = (args): React.ReactElement => {
     return <LockedVectorSettings {...args} />;
 };
 
-type StoryComponentType = StoryObj<typeof LockedVectorSettings>;
-
-// Set the default values in the control panel.
-Default.args = {
+const defaultProps = {
     ...getDefaultFigureForType("vector"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
+type StoryComponentType = StoryObj<typeof LockedVectorSettings>;
+
+// Set the default values in the control panel.
+Default.args = defaultProps;
+
 export const Expanded: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("vector"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
@@ -54,10 +54,7 @@ export const Expanded: StoryComponentType = {
  */
 export const WithInvalidPoints: StoryComponentType = {
     render: function Render() {
-        const [props, setProps] = React.useState({
-            ...getDefaultFigureForType("vector"),
-            onRemove: () => {},
-        });
+        const [props, setProps] = React.useState(defaultProps);
 
         const handlePropsUpdate = (newProps) => {
             setProps({
diff --git a/packages/perseus-editor/src/components/__tests__/locked-ellipse-settings.test.tsx b/packages/perseus-editor/src/components/__tests__/locked-ellipse-settings.test.tsx
index 04e9918758..566307c427 100644
--- a/packages/perseus-editor/src/components/__tests__/locked-ellipse-settings.test.tsx
+++ b/packages/perseus-editor/src/components/__tests__/locked-ellipse-settings.test.tsx
@@ -11,6 +11,7 @@ import type {UserEvent} from "@testing-library/user-event";
 const defaultProps = {
     ...getDefaultFigureForType("ellipse"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
diff --git a/packages/perseus-editor/src/components/__tests__/locked-line-settings.test.tsx b/packages/perseus-editor/src/components/__tests__/locked-line-settings.test.tsx
index 26e6f09d0c..32f4986e69 100644
--- a/packages/perseus-editor/src/components/__tests__/locked-line-settings.test.tsx
+++ b/packages/perseus-editor/src/components/__tests__/locked-line-settings.test.tsx
@@ -11,6 +11,7 @@ import type {UserEvent} from "@testing-library/user-event";
 const defaultProps = {
     ...getDefaultFigureForType("line"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
diff --git a/packages/perseus-editor/src/components/__tests__/locked-point-settings.test.tsx b/packages/perseus-editor/src/components/__tests__/locked-point-settings.test.tsx
index 7172038840..5ad1cf2a0e 100644
--- a/packages/perseus-editor/src/components/__tests__/locked-point-settings.test.tsx
+++ b/packages/perseus-editor/src/components/__tests__/locked-point-settings.test.tsx
@@ -11,6 +11,7 @@ import type {UserEvent} from "@testing-library/user-event";
 const defaultProps = {
     ...getDefaultFigureForType("point"),
     onRemove: () => {},
+    onMove: () => {},
     onChangeProps: () => {},
 };
 
diff --git a/packages/perseus-editor/src/components/__tests__/locked-polygon-settings.test.tsx b/packages/perseus-editor/src/components/__tests__/locked-polygon-settings.test.tsx
index a062b483c5..66c3c474e6 100644
--- a/packages/perseus-editor/src/components/__tests__/locked-polygon-settings.test.tsx
+++ b/packages/perseus-editor/src/components/__tests__/locked-polygon-settings.test.tsx
@@ -11,6 +11,7 @@ import type {UserEvent} from "@testing-library/user-event";
 const defaultProps = {
     ...getDefaultFigureForType("polygon"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 };
 
diff --git a/packages/perseus-editor/src/components/__tests__/locked-vector-settings.test.tsx b/packages/perseus-editor/src/components/__tests__/locked-vector-settings.test.tsx
index a9ff8caf3d..e1005b6968 100644
--- a/packages/perseus-editor/src/components/__tests__/locked-vector-settings.test.tsx
+++ b/packages/perseus-editor/src/components/__tests__/locked-vector-settings.test.tsx
@@ -12,6 +12,7 @@ import type {UserEvent} from "@testing-library/user-event";
 const defaultProps = {
     ...getDefaultFigureForType("vector"),
     onChangeProps: () => {},
+    onMove: () => {},
     onRemove: () => {},
 } as Props;
 
diff --git a/packages/perseus-editor/src/components/defining-point-settings.tsx b/packages/perseus-editor/src/components/defining-point-settings.tsx
index 17debd6f9a..dba6308f73 100644
--- a/packages/perseus-editor/src/components/defining-point-settings.tsx
+++ b/packages/perseus-editor/src/components/defining-point-settings.tsx
@@ -17,33 +17,41 @@ import CoordinatePairInput from "./coordinate-pair-input";
 import LabeledSwitch from "./labeled-switch";
 import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 
-import type {AccordionProps} from "./locked-figure-settings";
 import type {LockedPointType} from "@khanacademy/perseus";
 
-export type Props = AccordionProps &
-    LockedPointType & {
-        /**
-         * Optional label for the point to display in the header summary.
-         * Defaults to "Point".
-         */
-        label: string;
-        /**
-         * Whether the extra point settings are toggled open.
-         */
-        showPoint?: boolean;
-        /**
-         * Optional error message to display.
-         */
-        error?: string | null;
-        /**
-         * Called when the extra settings toggle switch is changed.
-         */
-        onTogglePoint?: (newValue) => void;
-        /**
-         * Called when the props (coords, color, etc.) are updated.
-         */
-        onChangeProps: (newProps: Partial<LockedPointType>) => void;
-    };
+export type Props = LockedPointType & {
+    /**
+     * Optional label for the point to display in the header summary.
+     * Defaults to "Point".
+     */
+    label: string;
+    /**
+     * Whether the extra point settings are toggled open.
+     */
+    showPoint?: boolean;
+    /**
+     * Optional error message to display.
+     */
+    error?: string | null;
+    /**
+     * Called when the extra settings toggle switch is changed.
+     */
+    onTogglePoint?: (newValue) => void;
+    /**
+     * Called when the props (coords, color, etc.) are updated.
+     */
+    onChangeProps: (newProps: Partial<LockedPointType>) => void;
+
+    // Accordion props
+    /**
+     * Whether this accordion is expanded.
+     */
+    expanded?: boolean;
+    /**
+     * Called when the accordion is expanded or collapsed.
+     */
+    onToggle?: (expanded: boolean) => void;
+};
 
 const DefiningPointSettings = (props: Props) => {
     const {
@@ -55,6 +63,8 @@ const DefiningPointSettings = (props: Props) => {
         error,
         onChangeProps,
         onTogglePoint,
+        expanded,
+        onToggle,
     } = props;
 
     function handleColorChange(newValue) {
@@ -63,8 +73,8 @@ const DefiningPointSettings = (props: Props) => {
 
     return (
         <LockedFigureSettingsAccordion
-            expanded={props.expanded}
-            onToggle={props.onToggle}
+            expanded={expanded}
+            onToggle={onToggle}
             containerStyle={styles.container}
             panelStyle={styles.accordionPanel}
             header={
diff --git a/packages/perseus-editor/src/components/locked-ellipse-settings.tsx b/packages/perseus-editor/src/components/locked-ellipse-settings.tsx
index 5e7c4bcab9..fe7fb4a9a8 100644
--- a/packages/perseus-editor/src/components/locked-ellipse-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-ellipse-settings.tsx
@@ -14,7 +14,7 @@ import EllipseSwatch from "./ellipse-swatch";
 import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 import LockedFigureSettingsActions from "./locked-figure-settings-actions";
 
-import type {AccordionProps} from "./locked-figure-settings";
+import type {LockedFigureSettingsCommonProps} from "./locked-figure-settings";
 import type {
     Coord,
     LockedFigureFillType,
@@ -24,12 +24,8 @@ import type {
 
 const {InfoTip} = components;
 
-export type Props = AccordionProps &
+export type Props = LockedFigureSettingsCommonProps &
     LockedEllipseType & {
-        /**
-         * Called when the delete button is pressed.
-         */
-        onRemove: () => void;
         /**
          * Called when the props (coords, color, etc.) are updated.
          */
@@ -47,6 +43,7 @@ const LockedEllipseSettings = (props: Props) => {
         expanded,
         onToggle,
         onChangeProps,
+        onMove,
         onRemove,
     } = props;
 
@@ -162,8 +159,9 @@ const LockedEllipseSettings = (props: Props) => {
 
             {/* Actions */}
             <LockedFigureSettingsActions
+                figureType={props.type}
+                onMove={onMove}
                 onRemove={onRemove}
-                figureAriaLabel={`locked ellipse at ${center[0]}, ${center[1]}`}
             />
         </LockedFigureSettingsAccordion>
     );
diff --git a/packages/perseus-editor/src/components/locked-figure-settings-actions.tsx b/packages/perseus-editor/src/components/locked-figure-settings-actions.tsx
index b8def139b6..dcdaa2e3e9 100644
--- a/packages/perseus-editor/src/components/locked-figure-settings-actions.tsx
+++ b/packages/perseus-editor/src/components/locked-figure-settings-actions.tsx
@@ -5,29 +5,76 @@
  */
 import Button from "@khanacademy/wonder-blocks-button";
 import {View} from "@khanacademy/wonder-blocks-core";
+import IconButton from "@khanacademy/wonder-blocks-icon-button";
+import {Spring} from "@khanacademy/wonder-blocks-layout";
 import {spacing} from "@khanacademy/wonder-blocks-tokens";
+import caretDoubleDownIcon from "@phosphor-icons/core/bold/caret-double-down-bold.svg";
+import caretDoubleUpIcon from "@phosphor-icons/core/bold/caret-double-up-bold.svg";
+import caretDownIcon from "@phosphor-icons/core/bold/caret-down-bold.svg";
+import caretUpIcon from "@phosphor-icons/core/bold/caret-up-bold.svg";
 import trashIcon from "@phosphor-icons/core/bold/trash-bold.svg";
 import {StyleSheet} from "aphrodite";
 import * as React from "react";
 
+import type {LockedFigureType} from "@khanacademy/perseus";
+
+export type LockedFigureSettingsMovementType =
+    | "back"
+    | "backward"
+    | "forward"
+    | "front";
+
 type Props = {
+    figureType: LockedFigureType;
+    onMove: (movement: LockedFigureSettingsMovementType) => void;
     onRemove: () => void;
-    figureAriaLabel: string;
 };
 
 const LockedFigureSettingsActions = (props: Props) => {
-    const {onRemove, figureAriaLabel} = props;
+    const {figureType, onMove, onRemove} = props;
+
     return (
         <View style={styles.container}>
             <Button
                 startIcon={trashIcon}
-                aria-label={`Delete ${figureAriaLabel}`}
+                aria-label={`Delete locked ${figureType}`}
                 onClick={onRemove}
                 kind="tertiary"
                 style={styles.deleteButton}
             >
                 Delete
             </Button>
+
+            <Spring />
+
+            <IconButton
+                icon={caretDoubleUpIcon}
+                size="small"
+                aria-label={`Move locked ${figureType} to the back`}
+                onClick={() => onMove("back")}
+                style={styles.iconButton}
+            />
+            <IconButton
+                icon={caretUpIcon}
+                size="small"
+                aria-label={`Move locked ${figureType} backward`}
+                onClick={() => onMove("backward")}
+                style={styles.iconButton}
+            />
+            <IconButton
+                icon={caretDownIcon}
+                size="small"
+                aria-label={`Move locked ${figureType} forward`}
+                onClick={() => onMove("forward")}
+                style={styles.iconButton}
+            />
+            <IconButton
+                icon={caretDoubleDownIcon}
+                size="small"
+                aria-label={`Move locked ${figureType} to the front`}
+                onClick={() => onMove("front")}
+                style={styles.iconButton}
+            />
         </View>
     );
 };
@@ -43,6 +90,11 @@ const styles = StyleSheet.create({
         // Line up the delete icon with the rest of the content.
         marginInlineStart: -spacing.xxxSmall_4,
     },
+    iconButton: {
+        // Reset the margin because the icon buttons
+        // overlap each other otherwise.
+        margin: 0,
+    },
 });
 
 export default LockedFigureSettingsActions;
diff --git a/packages/perseus-editor/src/components/locked-figure-settings.tsx b/packages/perseus-editor/src/components/locked-figure-settings.tsx
index ed3987e07b..9ca354b459 100644
--- a/packages/perseus-editor/src/components/locked-figure-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-figure-settings.tsx
@@ -14,15 +14,28 @@ import LockedPolygonSettings from "./locked-polygon-settings";
 import LockedVectorSettings from "./locked-vector-settings";
 
 import type {Props as LockedEllipseProps} from "./locked-ellipse-settings";
+import type {LockedFigureSettingsMovementType} from "./locked-figure-settings-actions";
 import type {Props as LockedLineProps} from "./locked-line-settings";
 import type {Props as LockedPointProps} from "./locked-point-settings";
 import type {Props as LockedPolygonProps} from "./locked-polygon-settings";
 import type {Props as LockedVectorProps} from "./locked-vector-settings";
 
-export type AccordionProps = {
+export type LockedFigureSettingsCommonProps = {
     // Whether to show the M2 features in the locked figure settings.
     // TODO(LEMS-2016): Remove this prop once the M2 flag is fully rolled out.
     showM2Features?: boolean;
+
+    // Movement props
+    /**
+     * Called when a movement button (top, up, down, bottom) is pressed.
+     */
+    onMove: (movement: LockedFigureSettingsMovementType) => void;
+    /**
+     * Called when the delete button is pressed.
+     */
+    onRemove: () => void;
+
+    // Accordion props
     /**
      * Whether this accordion is expanded.
      */
@@ -34,7 +47,7 @@ export type AccordionProps = {
 };
 
 // Union this type with other locked figure types when they are added.
-type Props = AccordionProps &
+type Props = LockedFigureSettingsCommonProps &
     (
         | LockedPointProps
         | LockedLineProps
diff --git a/packages/perseus-editor/src/components/locked-figures-section.tsx b/packages/perseus-editor/src/components/locked-figures-section.tsx
index 748d266a28..7770cda492 100644
--- a/packages/perseus-editor/src/components/locked-figures-section.tsx
+++ b/packages/perseus-editor/src/components/locked-figures-section.tsx
@@ -14,6 +14,7 @@ import LockedFigureSelect from "./locked-figure-select";
 import LockedFigureSettings from "./locked-figure-settings";
 import {getDefaultFigureForType} from "./util";
 
+import type {LockedFigureSettingsMovementType} from "./locked-figure-settings-actions";
 import type {Props as InteractiveGraphEditorProps} from "../widgets/interactive-graph-editor";
 import type {LockedFigure, LockedFigureType} from "@khanacademy/perseus";
 
@@ -47,6 +48,56 @@ const LockedFiguresSection = (props: Props) => {
         setExpandedStates([...expandedStates, true]);
     }
 
+    function moveLockedFigure(
+        index: number,
+        movement: LockedFigureSettingsMovementType,
+    ) {
+        // Don't allow moving the first figure up or the last figure down.
+        if (index === 0 && (movement === "back" || movement === "backward")) {
+            return;
+        }
+        if (
+            figures &&
+            index === figures.length - 1 &&
+            (movement === "front" || movement === "forward")
+        ) {
+            return;
+        }
+
+        const lockedFigures = figures || [];
+        const newFigures = [...lockedFigures];
+        const newExpandedStates = [...expandedStates];
+
+        // First, remove the figure from its current position
+        // in the figures array and the expanded states array.
+        const [removedFigure] = newFigures.splice(index, 1);
+        newExpandedStates.splice(index, 1);
+
+        // Then, add it back in the new position. Add "true" to the
+        // expanded states array for the new position (it must already
+        // be open since the button to move it is being pressed from there).
+        switch (movement) {
+            case "back":
+                newFigures.unshift(removedFigure);
+                newExpandedStates.unshift(true);
+                break;
+            case "backward":
+                newFigures.splice(index - 1, 0, removedFigure);
+                newExpandedStates.splice(index - 1, 0, true);
+                break;
+            case "forward":
+                newFigures.splice(index + 1, 0, removedFigure);
+                newExpandedStates.splice(index + 1, 0, true);
+                break;
+            case "front":
+                newFigures.push(removedFigure);
+                newExpandedStates.push(true);
+                break;
+        }
+        onChange({lockedFigures: newFigures});
+        setExpandedStates(newExpandedStates);
+    }
+
     function removeLockedFigure(index: number) {
         // eslint-disable-next-line no-alert
         if (window.confirm("Are you sure you want to delete this figure?")) {
@@ -110,6 +161,7 @@ const LockedFiguresSection = (props: Props) => {
                         onChangeProps={(newProps) =>
                             changeProps(index, newProps)
                         }
+                        onMove={(movement) => moveLockedFigure(index, movement)}
                         onRemove={() => removeLockedFigure(index)}
                     />
                 );
diff --git a/packages/perseus-editor/src/components/locked-line-settings.tsx b/packages/perseus-editor/src/components/locked-line-settings.tsx
index 94ed532adc..08aeb77c71 100644
--- a/packages/perseus-editor/src/components/locked-line-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-line-settings.tsx
@@ -19,7 +19,7 @@ import LineSwatch from "./line-swatch";
 import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 import LockedFigureSettingsActions from "./locked-figure-settings-actions";
 
-import type {AccordionProps} from "./locked-figure-settings";
+import type {LockedFigureSettingsCommonProps} from "./locked-figure-settings";
 import type {
     LockedFigure,
     LockedFigureColor,
@@ -30,11 +30,7 @@ import type {
 const lengthZeroStr = "The line cannot have length 0.";
 
 export type Props = LockedLineType &
-    AccordionProps & {
-        /**
-         * Called when the delete button is pressed.
-         */
-        onRemove: () => void;
+    LockedFigureSettingsCommonProps & {
         /**
          * Called when the props (points, color, etc.) are updated.
          */
@@ -50,6 +46,7 @@ const LockedLineSettings = (props: Props) => {
         showPoint1,
         showPoint2,
         onChangeProps,
+        onMove,
         onRemove,
     } = props;
     const [point1, point2] = points;
@@ -180,10 +177,9 @@ const LockedLineSettings = (props: Props) => {
 
             {/* Actions */}
             <LockedFigureSettingsActions
+                figureType={props.type}
+                onMove={onMove}
                 onRemove={onRemove}
-                figureAriaLabel={`locked line defined by
-                    ${point1.coord[0]}, ${point1.coord[1]} and
-                    ${point2.coord[0]}, ${point2.coord[1]}.`}
             />
         </LockedFigureSettingsAccordion>
     );
diff --git a/packages/perseus-editor/src/components/locked-point-settings.tsx b/packages/perseus-editor/src/components/locked-point-settings.tsx
index 0ff6de3dd7..5cfa2f868d 100644
--- a/packages/perseus-editor/src/components/locked-point-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-point-settings.tsx
@@ -18,15 +18,11 @@ import LabeledSwitch from "./labeled-switch";
 import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 import LockedFigureSettingsActions from "./locked-figure-settings-actions";
 
-import type {AccordionProps} from "./locked-figure-settings";
+import type {LockedFigureSettingsCommonProps} from "./locked-figure-settings";
 import type {LockedPointType} from "@khanacademy/perseus";
 
-export type Props = AccordionProps &
+export type Props = LockedFigureSettingsCommonProps &
     LockedPointType & {
-        /**
-         * Called when the delete button is pressed.
-         */
-        onRemove: () => void;
         /**
          * Called when the props (coords, color, etc.) are updated.
          */
@@ -39,6 +35,7 @@ const LockedPointSettings = (props: Props) => {
         color: pointColor,
         filled = true,
         onChangeProps,
+        onMove,
         onRemove,
     } = props;
 
@@ -82,8 +79,9 @@ const LockedPointSettings = (props: Props) => {
             />
 
             <LockedFigureSettingsActions
+                figureType={props.type}
+                onMove={onMove}
                 onRemove={onRemove}
-                figureAriaLabel={`locked point at ${coord[0]}, ${coord[1]}`}
             />
         </LockedFigureSettingsAccordion>
     );
diff --git a/packages/perseus-editor/src/components/locked-polygon-settings.tsx b/packages/perseus-editor/src/components/locked-polygon-settings.tsx
index 8bfbdd5dc0..9363448067 100644
--- a/packages/perseus-editor/src/components/locked-polygon-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-polygon-settings.tsx
@@ -24,14 +24,10 @@ import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 import LockedFigureSettingsActions from "./locked-figure-settings-actions";
 import PolygonSwatch from "./polygon-swatch";
 
-import type {AccordionProps} from "./locked-figure-settings";
+import type {LockedFigureSettingsCommonProps} from "./locked-figure-settings";
 
-export type Props = AccordionProps &
+export type Props = LockedFigureSettingsCommonProps &
     LockedPolygonType & {
-        /**
-         * Called when the delete button is pressed.
-         */
-        onRemove: () => void;
         /**
          * Called when the props (coords, color, etc.) are updated.
          */
@@ -48,6 +44,8 @@ const LockedPolygonSettings = (props: Props) => {
         expanded,
         onToggle,
         onChangeProps,
+        onMove,
+        onRemove,
     } = props;
 
     function handleColorChange(newValue: LockedFigureColor) {
@@ -199,8 +197,9 @@ const LockedPolygonSettings = (props: Props) => {
 
             {/* Actions */}
             <LockedFigureSettingsActions
-                onRemove={props.onRemove}
-                figureAriaLabel={`locked polygon with ${points.length} points`}
+                figureType={props.type}
+                onMove={onMove}
+                onRemove={onRemove}
             />
         </LockedFigureSettingsAccordion>
     );
diff --git a/packages/perseus-editor/src/components/locked-vector-settings.tsx b/packages/perseus-editor/src/components/locked-vector-settings.tsx
index d3a2ea9ac2..ba4253622a 100644
--- a/packages/perseus-editor/src/components/locked-vector-settings.tsx
+++ b/packages/perseus-editor/src/components/locked-vector-settings.tsx
@@ -18,7 +18,7 @@ import LineSwatch from "./line-swatch";
 import LockedFigureSettingsAccordion from "./locked-figure-settings-accordion";
 import LockedFigureSettingsActions from "./locked-figure-settings-actions";
 
-import type {AccordionProps} from "./locked-figure-settings";
+import type {LockedFigureSettingsCommonProps} from "./locked-figure-settings";
 import type {
     Coord,
     LockedFigure,
@@ -29,11 +29,7 @@ import type {
 const lengthErrorMessage = "The vector cannot have length 0.";
 
 export type Props = LockedVectorType &
-    AccordionProps & {
-        /**
-         * Called when the delete button is pressed.
-         */
-        onRemove: () => void;
+    LockedFigureSettingsCommonProps & {
         /**
          * Called when the props (points, color, etc.) are updated.
          */
@@ -41,7 +37,7 @@ export type Props = LockedVectorType &
     };
 
 const LockedVectorSettings = (props: Props) => {
-    const {points, color: lineColor, onChangeProps, onRemove} = props;
+    const {points, color: lineColor, onChangeProps, onMove, onRemove} = props;
     const [tail, tip] = points;
     const lineLabel = `Vector (${tail[0]}, ${tail[1]}), (${tip[0]}, ${tip[1]})`;
 
@@ -132,10 +128,9 @@ const LockedVectorSettings = (props: Props) => {
 
             {/* Actions */}
             <LockedFigureSettingsActions
+                figureType={props.type}
+                onMove={onMove}
                 onRemove={onRemove}
-                figureAriaLabel={`locked vector defined by starting point
-                    ${tail[0]}, ${tail[1]} and extending to
-                    ${tip[0]}, ${tip[1]}.`}
             />
         </LockedFigureSettingsAccordion>
     );
diff --git a/packages/perseus-editor/src/widgets/__tests__/interactive-graph-editor-locked-figures.test.tsx b/packages/perseus-editor/src/widgets/__tests__/interactive-graph-editor-locked-figures.test.tsx
index 26cc84aa8b..e5cd7caa54 100644
--- a/packages/perseus-editor/src/widgets/__tests__/interactive-graph-editor-locked-figures.test.tsx
+++ b/packages/perseus-editor/src/widgets/__tests__/interactive-graph-editor-locked-figures.test.tsx
@@ -97,7 +97,7 @@ describe("InteractiveGraphEditor locked figures", () => {
 
             // Act
             const deleteButton = screen.getByRole("button", {
-                name: /Delete/,
+                name: `Delete locked ${figureType}`,
             });
             await userEvent.click(deleteButton);
 
@@ -125,7 +125,7 @@ describe("InteractiveGraphEditor locked figures", () => {
 
             // Act
             const deleteButton = screen.getByRole("button", {
-                name: /Delete/,
+                name: `Delete locked ${figureType}`,
             });
             await userEvent.click(deleteButton);
 
@@ -134,6 +134,189 @@ describe("InteractiveGraphEditor locked figures", () => {
             expect(onChangeMock).not.toBeCalled();
         });
 
+        describe("movement", () => {
+            const first = {
+                ...getDefaultFigureForType(figureType),
+                color: "blue",
+            };
+            const second = {
+                ...getDefaultFigureForType(figureType),
+                color: "green",
+            };
+            const third = {
+                ...getDefaultFigureForType(figureType),
+                color: "red",
+            };
+
+            test(`Calls onChange when a locked ${figureType} is moved back`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} to the back`,
+                });
+                await userEvent.click(moveButton[2]);
+
+                // Assert
+                expect(onChangeMock).toBeCalledWith(
+                    expect.objectContaining({
+                        lockedFigures: [third, first, second],
+                    }),
+                );
+            });
+
+            test(`Calls onChange when a locked ${figureType} is moved backward`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} backward`,
+                });
+                await userEvent.click(moveButton[2]);
+
+                // Assert
+                expect(onChangeMock).toBeCalledWith(
+                    expect.objectContaining({
+                        lockedFigures: [first, third, second],
+                    }),
+                );
+            });
+
+            test(`Calls onChange when a locked ${figureType} is moved forward`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} forward`,
+                });
+                await userEvent.click(moveButton[0]);
+
+                // Assert
+                expect(onChangeMock).toBeCalledWith(
+                    expect.objectContaining({
+                        lockedFigures: [second, first, third],
+                    }),
+                );
+            });
+
+            test(`Calls onChange when a locked ${figureType} is moved front`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} to the front`,
+                });
+                await userEvent.click(moveButton[0]);
+
+                // Assert
+                expect(onChangeMock).toBeCalledWith(
+                    expect.objectContaining({
+                        lockedFigures: [second, third, first],
+                    }),
+                );
+            });
+
+            test(`Does not call onChange when a locked ${figureType} is moved to the back and is already in the back`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} to the back`,
+                });
+                await userEvent.click(moveButton[0]);
+
+                // Assert
+                expect(onChangeMock).not.toBeCalled();
+            });
+
+            test(`Does not call onChange when a locked ${figureType} is moved backward and is already in the back`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} backward`,
+                });
+                await userEvent.click(moveButton[0]);
+
+                // Assert
+                expect(onChangeMock).not.toBeCalled();
+            });
+
+            test(`Does not call onChange when a locked ${figureType} is moved forward and is already in the front`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} forward`,
+                });
+                await userEvent.click(moveButton[2]);
+
+                // Assert
+                expect(onChangeMock).not.toBeCalled();
+            });
+
+            test(`Does not call onChange when a locked ${figureType} is moved to the front and is already in the front`, async () => {
+                // Arrange
+                const onChangeMock = jest.fn();
+
+                renderEditor({
+                    onChange: onChangeMock,
+                    lockedFigures: [first, second, third],
+                });
+
+                // Act
+                const moveButton = screen.getAllByRole("button", {
+                    name: `Move locked ${figureType} to the front`,
+                });
+                await userEvent.click(moveButton[2]);
+
+                // Assert
+                expect(onChangeMock).not.toBeCalled();
+            });
+        });
+
         test("Shows settings accordion when a locked $figureType is passed in", async () => {
             // Arrange
             renderEditor({
@@ -996,7 +1179,7 @@ describe("InteractiveGraphEditor locked figures", () => {
 
             // Delete the figure
             const deleteButton = screen.getByRole("button", {
-                name: "Delete locked line defined by 0, 0 and 2, 2.",
+                name: "Delete locked line",
             });
             await userEvent.click(deleteButton);