Question

The coordinates of a rectangle are (4, 0), (8, 0), (4, 10) and (8, 10). Which transformation results in a reduction in the size of a rectangle?

A) The rectangle reflects across the y-axis.

B) The rectangle undergoes a dilation by a scale factor of 2.

C) The rectangle translates 3 units to the left and 6 units up.

D) The rectangle undergoes a dilation by a scale factor of 0.5.

Answer 1

D) The rectangle undergoes a dilation by a scale factor of 0.5.

Explanation:

A translation is only a slide; it does not change the size of a figure.

A reflection creates a mirror image; it does not change the size of a figure.

A rotation turns a figure; it does not change the size of a figure.

A dilation is a stretch or shrink, which by definition changes the size of a figure.

A dilation by a factor greater than 1 will stretch a figure, and a dilation by a factor less than 1 (but greater than 0) will shrink a figure. Since we want a reduction in size, we want a shrink; this means out of all of our options, the only correct one is a dilation by a factor of 0.5.