Question

The vertices of a square are located at (0, 2), (2, 0), (0, -2), and (-2, 0).

Select all transformations that will carry this square onto itself.
A reflection across the line y = x
B reflection across the line y = -X
C reflection across the x-axis
D 45° rotation about the origin
E 90° rotation about the origin

Answer 1

Explanation:

A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.

A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.

However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.

A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.

Therefore, the correct answers are C, D, and E.