Question

which statement shows why rectangle wxyz is congruent to rectangle wxyz?
a. the rectangle was rotated 90° clockwise about the origin and shifted 3 units in the y direction.
b. the rectangle was rotated 180° clockwise about the origin and shifted 3 units in the y direction.
c. the rectangle was rotated 180° clockwise about the origin and shifted 3 units in the x direction.
d. the rectangle was rotated 90° clockwise about the origin and shifted 3 units in the x direction.

Explanation:

When a rectangle is rotated \(90^{\circ}\) clockwise about the origin, its orientation changes. Then, shifting it \(3\) units in the \(y\) - direction moves it vertically. Rotation and translation (shifting) are rigid transformations. Rigid transformations preserve the shape and size of the figure, which means the pre - image (original rectangle \(WXYZ\)) and the image (new rectangle \(W'X'Y'Z'\)) are congruent.

Answer:

A. The rectangle was rotated \(90^{\circ}\) clockwise about the origin and shifted \(3\) units in the \(y\) direction.