Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated using the rule $(x, y) \rightarrow \left(\frac{1}{4}x, \frac{1}{4}y\right)$ to create pentagon M'N'P'Q'R'. Which statement is true?

A. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

B. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

C. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

D. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

The correct answer is b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR because the scale factor of 1/4 is less than 1, resulting in a proportionally smaller figure after the dilation.

Explanation:

The student asked which statement is true when pentagon MNPQR is dilated using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'. The correct answer to this question is b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1. When we dilate a figure by a scale factor that is less than 1, we create a smaller figure, proportional to the original.

It's important to note that scale factor indicates a multiplicative change. Since the scale factor given in the question is 1/4, which is less than 1, the resulting pentagon M'N'P'Q'R' is indeed smaller than the original pentagon MNPQR. This concept is a fundamental aspect of geometric transformations, specifically dilations.