diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h
index 00b7c4300..ad5b6e666 100644
--- a/Eigen/src/Geometry/Hyperplane.h
+++ b/Eigen/src/Geometry/Hyperplane.h
@@ -218,7 +218,10 @@ public:
   inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
   {
     if (traits==Affine)
+    {
       normal() = mat.inverse().transpose() * normal();
+      m_coeffs /= normal().norm();
+    }
     else if (traits==Isometry)
       normal() = mat * normal();
     else
diff --git a/test/geo_hyperplane.cpp b/test/geo_hyperplane.cpp
index 327537801..617407d21 100644
--- a/test/geo_hyperplane.cpp
+++ b/test/geo_hyperplane.cpp
@@ -59,12 +59,15 @@ template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
     VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
     pl2 = pl1;
     VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
+    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
     pl2 = pl1;
     VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
                                  .absDistance((rot*scaling*translation) * p1), Scalar(1) );
+    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
     pl2 = pl1;
     VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
                                  .absDistance((rot*translation) * p1), Scalar(1) );
+    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
   }
 
   // casting