Invariant Points

Invariant points are points which do not move when a single transformation or multiple transformations occur.

Quite simply it's any point that is still in the same place as where it was before the transformation occured.

It doesn't necessarily have to be a point on the shape.

There can also be more than one invariant point.

Make sure you are confident with performing transformations before attempting this topic.

In the example question the triangle has been reflected in the line and the blue point is in the same position even after the reflection. So the blue point is invariant.

Example Question

Triangle A is transformed by the combined transformation of a rotation of 180° about the point(-2, 0) followed by a translation with vector(-3   2)

One point on triangle A is invariant under the combined transformation.

Find the coordinates of this point.