Invariant Points Demonstration This resource provides animated demonstrations

Invariant Points – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

A This vertex does not change: it is an invariant point.

If we enlarge Triangle B using a scale factor of 3 & the centre of enlargement (1, 1), what changes & what stays the same? B This vertex does not change: it is an invariant point.

If we rotate Triangle C 90° clockwise about point (− 2, 1), what changes & what stays the same? This vertex does not change: it is an invariant point. C

D There are no invariant points with this transformation.

State the invariant point (if any) with these transformations. Plot the transformation to check. 1) A B 2) B A C C (2, 1) (4, 1) Triangle ABC rotated 90° clockwise about point (2, 1) 3) 4) (3, − 6) B B A C A C Triangle ABC enlarged by a scale factor 2, centre of enlargement (3, − 6).

E (2, 2) & (2, 3) Invariant points do not need to be vertices. They can be on any side but are not within a shape.

F (0, 0) & (3, 3) Invariant points do not need to be vertices. They can be on any side but are not within a shape.

True or False? There will always be an invariant point when you rotate a shape around a vertex. A translated shape will never have an invariant point. There will always be an invariant point when we enlarge a shape using an external centre of enlargement. A shape rotated around an external point will never have an invariant point. A polygon reflected in one of its sides will always have exactly two invariant points. 2 or more

State the invariant points (if any) with these transformations. (8, 12) (4, 12) (10, 11) (10, 9) (8, 3) (14, 3) (2, 5) (10, 5) Rotation 180° around the point (10, 9). (5, 7) (2, 5) (5, 5) (2, 2) (7, 2) (5, 2) (3, 1) Enlargement by scale factor 4 with centre of enlargement (4, 2)

a) For each shape, state a transformation that has exactly 1 invariant point. (4, 12) (14, 12) (4, 3) (10, 11) (2, 5) (10, 5) (5, 7) (2, 5) (2, 2) (7, 2) (5, 2) (3, 1) b) For each shape, state a transformation that has exactly 2 invariant points.

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk