Determine the coordinates of the vertices of the rotation image of the trapezoid ABCD

Question

Determine the coordinates of the vertices of the rotation image of the trapezoid ABCD (in the figure) if it is rotated 90 degrees clockwise about point X.

Answer 1

Making X at (0, 0), then

A (2, 0)

B (2, 2,)

C (3, 2)

D (5, 0)

R₉₀ (x, y) → (y, -x)

With respect to X

A' (0, -2)

B' (2, -2)

C' (2, -3)

D' (0, -5)

Answer 2

First rotate the trapezoid 90 degrees clockwise about point A.

Doing so will result in a trapezoid with vertices of: A(4,7), B(6,7), C(6,6) and D(4,4).

Lastly, move the x coordinate of each vertex by the value of -2 since point X is -2 away from point A.

This results in a trapezoid with vertices of: A(2,7), B(4,7), C(4,6) and D(2,4).