Question

Find a transformation of the polygon that does not result in a diagram with line symmetry or rotational symmetry. Draw the image and list the coordinates of the vertices of the larger shape. How do you know the diagram does not have symmetry?

Answer 1

A rotation ${90}^o$ clockwise about the point (2,4) does not result in a diagram that has line symmetry or rotational symmetry.

Coordinates of the larger shape : A(2,8), B(4,10), C(6,8), D(8,10), E(10,8), F(10,4),

A'(6,4), B'(8,2), C'(6,0), D'(8,-2), E'(6,-4), F'(2,-4)

The diagram does not have line symmetry because there is no line on which a mirror can be placed so that the polygon is the reflection of the other. The diagram does not have rotational symmetry because there is no point about which it can be rotated so that it coincides with itself.