Question

Which series of transformations shows that rectangle A is similar to rectangle B?

A. Reflect rectangle A over the y-axis and dilate it by a scale factor of 3 with the center of dilation at the origin.
B. Dilate rectangle A by a scale factor of 2 with the center of dilation at the origin and rotate it 180° clockwise about the origin.
C. Translate rectangle A 5 units up and dilate it by a scale factor of 3 with the center of dilation at the origin.
D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.

Answer 1

D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.

Explanation:

We are two rectangles, A and B, and to determine whether which series of transformations show that A is similar to rectangle B.

The coordinates of rectangle A are: (1, 1), (1, -1), (-2, 1) and (-2, -1) while the coordinates of the rectangle B are: (3, 6), (3, -3), ((-3, 6) and (-3, -3).

To transform rectangle A into rectangle B, we need to dilate A by a scale factor 3 and then rotate it 90 degrees clockwise through the origin.

Therefore, the correct answer option is D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.

Answer 2

D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.

Explanation:

The coordinates of triangle A are (-2,1) , (1,1), (1,-1) and (-2, -1) while that of triangle B are (-3, 6), (3, 6), (3, -3) and (-3, 3).

To transform A to be we need a combination of two transformations, and that is dilation and rotation.

If A is dilated by a scale factor three through the origin as the center of dilation and then rotated through 90° clockwise with the origin as the center of origin, then rectangle B will be obtained.