Question

Pentagon G'P'E'ST' is dilated with the origin as the center of dilation using the rule (x, y) → (0.21x, 0.2y) to create pentagon G'P'E'ST'. Which statement is true?

A. Pentagon G'P'E'ST' is larger than pentagon GPEST because the scale factor is greater than 1.
B. Pentagon G'P'E'ST' is larger than pentagon GPEST because the scale factor is less than 1.
C. Pentagon G'P'E'ST' is smaller than pentagon GPEST because the scale factor is greater than 1.
D. Pentagon G'P'E'ST' is smaller than pentagon GPEST because the scale factor is less than 1.

Answer 1

Pentagon G'P'E'ST' is smaller than pentagon GPEST because the scale factor used for dilation, 0.21 and 0.2, are both less than 1, leading to a reduction in size.

Step-by-step explanation:

When a pentagon GPEST is dilated using the rule (x, y) → (0.21x, 0.2y), we are applying a scale factor to each coordinate of the pentagon's vertices. The scale factors given, 0.21 and 0.2, are both less than 1. This indicates that each coordinate of the pentagon's vertices will be multiplied by a number less than 1, resulting in a new pentagon, G'P'E'ST', that is smaller than the original pentagon GPEST. Therefore, the correct statement is D. Pentagon G'P'E'ST' is smaller than pentagon GPEST because the scale factor is less than 1.