Question

Rectangle RSFT has vertices R(3,10), S(5,10), F(5,6) and T(3,6). RSFT was reflected over the line

y = x, to form R'S'F'T'. What are the coordinates of the vertices of the image?

Answer 1

The coordinates of the vertices of the image are R' (10, 3), S' (10, 5), F' (6, 5), T' (6, 3)

Explanation:

• If the point (x, y) reflected across the line y = x, then its image is (y, x)

• If the point (x, y) reflected across the line y = -x, then its image is (-y, -x)

Let us use the first rule above to solve the question.

∵ Rectangle RSFT has vertices R (3, 10), S (5, 10), F (5, 6), and T(3, 6)

∵ RSFT was reflected over the line, y = x

→ To find its image switch the coordinates of all the vertices

∵ R = (3, 10)

∴ R' = (10, 3)

∵ S = (5, 10)

∴ S' = (10, 5)

∵ F = (5, 6)

∴ F' = (6, 5)

∵ T = (3, 6)

∴ T' = (6, 3)

The coordinates of the vertices of the image are R' (10, 3), S' (10, 5), F' (6, 5), T' (6, 3)