diff --git a/src/material/legacy-tooltip/tooltip.spec.ts b/src/material/legacy-tooltip/tooltip.spec.ts
index e64798260154..b8c90ea7a4c0 100644
--- a/src/material/legacy-tooltip/tooltip.spec.ts
+++ b/src/material/legacy-tooltip/tooltip.spec.ts
@@ -237,7 +237,7 @@ describe('MatTooltip', () => {
       TestBed.resetTestingModule()
         .configureTestingModule({
           imports: [MatLegacyTooltipModule, OverlayModule],
-          declarations: [WideTooltipDemo]
+          declarations: [WideTooltipDemo],
         })
         .compileComponents();
 
@@ -254,8 +254,12 @@ describe('MatTooltip', () => {
       tick();
       expect(tooltipDirective._isTooltipVisible()).toBe(true);
 
-      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeGreaterThan(triggerRect.left + 200);
-      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeLessThan(triggerRect.left + 300);
+      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeGreaterThan(
+        triggerRect.left + 200,
+      );
+      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeLessThan(
+        triggerRect.left + 300,
+      );
       expect(tooltipDirective._overlayRef!.overlayElement.offsetTop).toBe(triggerRect.bottom);
     }));
 
@@ -1227,10 +1231,7 @@ describe('MatTooltip', () => {
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
 
-      const triggerRect = button.getBoundingClientRect();
-      const offsetX = triggerRect.right - 10;
-      const offsetY = triggerRect.top + 10;
-      dispatchTouchEvent(button, 'touchstart', offsetX, offsetY, offsetX, offsetY);
+      dispatchFakeEvent(button, 'touchstart');
       fixture.detectChanges();
       tick(250); // Halfway through the delay.
 
@@ -1249,10 +1250,7 @@ describe('MatTooltip', () => {
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
 
-      const triggerRect = button.getBoundingClientRect();
-      const offsetX = triggerRect.right - 10;
-      const offsetY = triggerRect.top + 10;
-      dispatchTouchEvent(button, 'touchstart', offsetX, offsetY, offsetX, offsetY);
+      dispatchFakeEvent(button, 'touchstart');
       fixture.detectChanges();
       tick(500); // Finish the delay.
       fixture.detectChanges();
@@ -1265,10 +1263,7 @@ describe('MatTooltip', () => {
       const fixture = TestBed.createComponent(BasicTooltipDemo);
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
-      const triggerRect = button.getBoundingClientRect();
-      const offsetX = triggerRect.right - 10;
-      const offsetY = triggerRect.top + 10;
-      const event = dispatchTouchEvent(button, 'touchstart', offsetX, offsetY, offsetX, offsetY);
+      const event = dispatchFakeEvent(button, 'touchstart');
       fixture.detectChanges();
 
       expect(event.defaultPrevented).toBe(false);
@@ -1279,10 +1274,7 @@ describe('MatTooltip', () => {
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
 
-      const triggerRect = button.getBoundingClientRect();
-      const offsetX = triggerRect.right - 10;
-      const offsetY = triggerRect.top + 10;
-      dispatchTouchEvent(button, 'touchstart', offsetX, offsetY, offsetX, offsetY);
+      dispatchFakeEvent(button, 'touchstart');
       fixture.detectChanges();
       tick(500); // Finish the open delay.
       fixture.detectChanges();
@@ -1306,10 +1298,7 @@ describe('MatTooltip', () => {
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
 
-      const triggerRect = button.getBoundingClientRect();
-      const offsetX = triggerRect.right - 10;
-      const offsetY = triggerRect.top + 10;
-      dispatchTouchEvent(button, 'touchstart', offsetX, offsetY, offsetX, offsetY);
+      dispatchFakeEvent(button, 'touchstart');
       fixture.detectChanges();
       tick(500); // Finish the open delay.
       fixture.detectChanges();
@@ -1474,9 +1463,8 @@ describe('MatTooltip', () => {
       const fixture = TestBed.createComponent(BasicTooltipDemo);
       fixture.detectChanges();
       const button: HTMLButtonElement = fixture.nativeElement.querySelector('button');
-      const triggerRect = button.getBoundingClientRect();
 
-      dispatchMouseEvent(button, 'mouseenter', triggerRect.right - 10, triggerRect.top + 10);
+      dispatchFakeEvent(button, 'mouseenter');
       fixture.detectChanges();
       tick(500); // Finish the open delay.
       fixture.detectChanges();
@@ -1484,6 +1472,7 @@ describe('MatTooltip', () => {
       assertTooltipInstance(fixture.componentInstance.tooltip, true);
 
       // Simulate the pointer over the trigger.
+      const triggerRect = button.getBoundingClientRect();
       const wheelEvent = createFakeEvent('wheel');
       Object.defineProperties(wheelEvent, {
         clientX: {get: () => triggerRect.left + 1},
diff --git a/src/material/tooltip/tooltip.spec.ts b/src/material/tooltip/tooltip.spec.ts
index c44feb0266ce..d2b88c27cb9b 100644
--- a/src/material/tooltip/tooltip.spec.ts
+++ b/src/material/tooltip/tooltip.spec.ts
@@ -239,7 +239,7 @@ describe('MDC-based MatTooltip', () => {
       TestBed.resetTestingModule()
         .configureTestingModule({
           imports: [MatTooltipModule, OverlayModule],
-          declarations: [WideTooltipDemo]
+          declarations: [WideTooltipDemo],
         })
         .compileComponents();
 
@@ -256,8 +256,12 @@ describe('MDC-based MatTooltip', () => {
       tick();
       expect(tooltipDirective._isTooltipVisible()).toBe(true);
 
-      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeLessThan(triggerRect.right - 250);
-      expect(tooltipDirective._overlayRef!.overlayElement.offsetTop).toBeGreaterThanOrEqual(triggerRect.bottom);
+      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBeLessThan(
+        triggerRect.right - 250,
+      );
+      expect(tooltipDirective._overlayRef!.overlayElement.offsetTop).toBeGreaterThanOrEqual(
+        triggerRect.bottom,
+      );
     }));
 
     it('should be able to override the default positionAtOrigin', fakeAsync(() => {
@@ -287,7 +291,9 @@ describe('MDC-based MatTooltip', () => {
       tick();
       expect(tooltipDirective._isTooltipVisible()).toBe(true);
 
-      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBe(triggerRect.right - 100 - 20);
+      expect(tooltipDirective._overlayRef!.overlayElement.offsetLeft).toBe(
+        triggerRect.right - 100 - 20,
+      );
       expect(tooltipDirective._overlayRef!.overlayElement.offsetTop).toBe(triggerRect.top + 100);
     }));
 
diff --git a/src/material/tooltip/tooltip.ts b/src/material/tooltip/tooltip.ts
index c0dfeda735c0..806e8b181675 100644
--- a/src/material/tooltip/tooltip.ts
+++ b/src/material/tooltip/tooltip.ts
@@ -407,7 +407,7 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
   }
 
   /** Shows the tooltip after the delay in ms, defaults to tooltip-delay-show or 0ms if no input */
-  show(delay: number = this.showDelay, origin?: { x: number, y: number }): void {
+  show(delay: number = this.showDelay, origin?: {x: number; y: number}): void {
     if (
       this.disabled ||
       !this.message ||
@@ -442,7 +442,7 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
   }
 
   /** Shows/hides the tooltip */
-  toggle(origin?: { x: number; y: number; }): void {
+  toggle(origin?: {x: number; y: number}): void {
     this._isTooltipVisible() ? this.hide() : this.show(undefined, origin);
   }
 
@@ -452,10 +452,10 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
   }
 
   /** Create the overlay config and position strategy */
-  private _createOverlay(origin?: { x: number; y: number; }): OverlayRef {
+  private _createOverlay(origin?: {x: number; y: number}): OverlayRef {
     if (this._overlayRef) {
-      const existingStrategy =
-        this._overlayRef.getConfig().positionStrategy as FlexibleConnectedPositionStrategy;
+      const existingStrategy = this._overlayRef.getConfig()
+        .positionStrategy as FlexibleConnectedPositionStrategy;
 
       if ((!this.positionAtOrigin || !origin) && existingStrategy._origin instanceof ElementRef) {
         return this._overlayRef;
@@ -471,7 +471,7 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
     // Create connected position strategy that listens for scroll events to reposition.
     const strategy = this._overlay
       .position()
-      .flexibleConnectedTo(this.positionAtOrigin ? (origin || this._elementRef) : this._elementRef)
+      .flexibleConnectedTo(this.positionAtOrigin ? origin || this._elementRef : this._elementRef)
       .withTransformOriginOn(`.${this._cssClassPrefix}-tooltip`)
       .withFlexibleDimensions(false)
       .withViewportMargin(this._viewportMargin)
@@ -716,7 +716,11 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
         'mouseenter',
         event => {
           this._setupPointerExitEventsIfNeeded();
-          this.show(undefined, { x: (event as MouseEvent).x, y: (event as MouseEvent).y });
+          let point = undefined;
+          if ((event as MouseEvent).x !== undefined && (event as MouseEvent).y !== undefined) {
+            point = event as MouseEvent;
+          }
+          this.show(undefined, point);
         },
       ]);
     } else if (this.touchGestures !== 'off') {
@@ -725,8 +729,8 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase>
       this._passiveListeners.push([
         'touchstart',
         event => {
-          const touch = (event as TouchEvent).targetTouches[0];
-          const origin = touch ? { x: touch.clientX, y: touch.clientY } : undefined;
+          const touch = (event as TouchEvent).targetTouches?.[0];
+          const origin = touch ? {x: touch.clientX, y: touch.clientY} : undefined;
           // Note that it's important that we don't `preventDefault` here,
           // because it can prevent click events from firing on the element.
           this._setupPointerExitEventsIfNeeded();
diff --git a/tools/public_api_guard/cdk/overlay.md b/tools/public_api_guard/cdk/overlay.md
index a2ccaee9a40d..31371ac3d2db 100644
--- a/tools/public_api_guard/cdk/overlay.md
+++ b/tools/public_api_guard/cdk/overlay.md
@@ -184,6 +184,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
     // (undocumented)
     detach(): void;
     dispose(): void;
+    _origin: FlexibleConnectedPositionStrategyOrigin;
     positionChanges: Observable<ConnectedOverlayPositionChange>;
     get positions(): ConnectionPositionPair[];
     _preferredPositions: ConnectionPositionPair[];
diff --git a/tools/public_api_guard/material/tooltip.md b/tools/public_api_guard/material/tooltip.md
index 531b85e0e7ea..7dba5dde8140 100644
--- a/tools/public_api_guard/material/tooltip.md
+++ b/tools/public_api_guard/material/tooltip.md
@@ -107,10 +107,19 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase> implement
     _overlayRef: OverlayRef | null;
     get position(): TooltipPosition;
     set position(value: TooltipPosition);
-    show(delay?: number): void;
+    // (undocumented)
+    get positionAtOrigin(): boolean;
+    set positionAtOrigin(value: BooleanInput);
+    show(delay?: number, origin?: {
+        x: number;
+        y: number;
+    }): void;
     get showDelay(): number;
     set showDelay(value: NumberInput);
-    toggle(): void;
+    toggle(origin?: {
+        x: number;
+        y: number;
+    }): void;
     get tooltipClass(): string | string[] | Set<string> | {
         [key: string]: any;
     };
@@ -125,7 +134,7 @@ export abstract class _MatTooltipBase<T extends _TooltipComponentBase> implement
     // (undocumented)
     protected _viewportMargin: number;
     // (undocumented)
-    static ɵdir: i0.ɵɵDirectiveDeclaration<_MatTooltipBase<any>, never, never, { "position": "matTooltipPosition"; "disabled": "matTooltipDisabled"; "showDelay": "matTooltipShowDelay"; "hideDelay": "matTooltipHideDelay"; "touchGestures": "matTooltipTouchGestures"; "message": "matTooltip"; "tooltipClass": "matTooltipClass"; }, {}, never, never, false>;
+    static ɵdir: i0.ɵɵDirectiveDeclaration<_MatTooltipBase<any>, never, never, { "position": "matTooltipPosition"; "positionAtOrigin": "matTooltipPositionAtOrigin"; "disabled": "matTooltipDisabled"; "showDelay": "matTooltipShowDelay"; "hideDelay": "matTooltipHideDelay"; "touchGestures": "matTooltipTouchGestures"; "message": "matTooltip"; "tooltipClass": "matTooltipClass"; }, {}, never, never, false>;
     // (undocumented)
     static ɵfac: i0.ɵɵFactoryDeclaration<_MatTooltipBase<any>, never>;
 }
@@ -135,6 +144,7 @@ export interface MatTooltipDefaultOptions {
     disableTooltipInteractivity?: boolean;
     hideDelay: number;
     position?: TooltipPosition;
+    positionAtOrigin?: boolean;
     showDelay: number;
     touchendHideDelay: number;
     touchGestures?: TooltipTouchGestures;