diff --git a/packages/flutter/lib/src/rendering/box.dart b/packages/flutter/lib/src/rendering/box.dart
index f2a776f6b58..171d0ce84d0 100644
--- a/packages/flutter/lib/src/rendering/box.dart
+++ b/packages/flutter/lib/src/rendering/box.dart
@@ -636,6 +636,9 @@ abstract class RenderBox extends RenderObject {
 
   /// Convert the given point from the global coodinate system to the local
   /// coordinate system for this box.
+  ///
+  /// If the transform from global coordinates to local coordinates is
+  /// degenerate, this function returns Point.origin.
   Point globalToLocal(Point point) {
     assert(attached);
     Matrix4 transform = new Matrix4.identity();
@@ -645,8 +648,9 @@ abstract class RenderBox extends RenderObject {
       rendererParent.applyPaintTransform(renderer, transform);
       renderer = rendererParent;
     }
-    /* double det = */ transform.invert();
-    // TODO(abarth): Check the determinant for degeneracy.
+    double det = transform.invert();
+    if (det == 0.0)
+      return Point.origin;
     return _transformPoint(transform, point);
   }
 
diff --git a/packages/flutter/lib/src/rendering/proxy_box.dart b/packages/flutter/lib/src/rendering/proxy_box.dart
index 07b1855a12e..ac1e8b9bf37 100644
--- a/packages/flutter/lib/src/rendering/proxy_box.dart
+++ b/packages/flutter/lib/src/rendering/proxy_box.dart
@@ -991,9 +991,14 @@ class RenderTransform extends RenderProxyBox {
 
   bool hitTest(HitTestResult result, { Point position }) {
     if (transformHitTests) {
-      Matrix4 inverse = new Matrix4.zero();
-      // TODO(abarth): Check the determinant for degeneracy.
-      inverse.copyInverse(_effectiveTransform);
+      Matrix4 inverse;
+      try {
+        inverse = new Matrix4.inverted(_effectiveTransform);
+      } catch (e) {
+        // We cannot invert the effective transform. That means the child
+        // doesn't appear on screen and cannot be hit.
+        return false;
+      }
       Vector3 position3 = new Vector3(position.x, position.y, 0.0);
       Vector3 transformed3 = inverse.transform3(position3);
       position = new Point(transformed3.x, transformed3.y);
diff --git a/packages/flutter/pubspec.yaml b/packages/flutter/pubspec.yaml
index aca4524a81c..c33631bda35 100644
--- a/packages/flutter/pubspec.yaml
+++ b/packages/flutter/pubspec.yaml
@@ -10,7 +10,7 @@ dependencies:
   material_design_icons: '>=0.0.3 <0.1.0'
   sky_engine: 0.0.81
   sky_services: 0.0.81
-  vector_math: '>=1.4.3 <2.0.0'
+  vector_math: '>=1.4.5 <2.0.0'
   quiver: '>=0.21.4 <0.22.0'
 
   # See the comment in flutter_tools' pubspec.yaml. We have to pin it