What is an invariant point?
Invariant points are points on a line or shape which do not move when a specific transformation is applied.
They are sometimes also referred to as fixed points.
Points which are invariant under one transformation may not be invariant under a different transformation.
When do invariant points occur?
This depends on the transformation in question:
1) Reflection: Invariant points occur if the mirror line touches the shape;
2) Rotation: Invariant points occur when the centre of rotation is on one of the edges or vertices of the shape to be rotated;
3) Enlargement: Invariant points occur when the centre of enlargement is on one of the edges or vertices of the shape to be enlarged;
4) Translations: Invariant points cannot occur on a translation, as every point needs to move the same amount.
Now let's see how we get on with identifying these scenarios in real contexts.
In this activity, we will identify invariant points in theory and in practice in problems involving geometric reflection, rotation and enlargement.
You may want to have a pencil and piece of squared paper handy, so that you can draw out some of the transformations described above. If you do not have this, then you will have to imagine the movements taking place in your mind's eye.