Question

Pentagon WFNSC is shown on the coordinate grid. Pentagon WFNSC is dilated with the origin as the center of dilation using the rule (x, y) = (3x, 3y) to create pentagon W'F'N'S'C'.

Which statement is true?
a. Pentagon W'F'N'S'C' is larger than pentagon WFNSC because the scale factor is greater than 1.
b. Pentagon W'F'N'S'C' is larger than pentagon WFNSC because the scale factor is less than 1.
c. Pentagon W'F'N'S'C' is smaller than pentagon WFNSC because the scale factor is less than 1.
d. Pentagon W'F'N'S'C' is smaller than pentagon WFNSC because the scale factor is greater than 1.

Answer 1

The dilation of pentagon WFNSC with the rule (x, y) = (3x, 3y) makes pentagon W'F'N'S'C' larger as the scale factor of 3 indicates enlarging.

Step-by-step explanation:

The question is about the effects of dilation on a pentagon using the rule (x, y) = (3x, 3y). This rule means that the scale factor of the dilation is 3. A scale factor greater than 1 indicates that the figure will be enlarged. Therefore, the correct answer is that pentagon W'F'N'S'C' is larger than pentagon WFNSC because the scale factor is greater than 1, which corresponds to option a. When dilating a figure using the origin as the center of dilation, the scale factor determines if the resulting figure is larger or smaller than the original figure.

In this case, the scale factor is (x, y) = (3x, 3y). Since both x and y are multiplied by 3, the scale factor is greater than 1. This means that the resulting pentagon, W'F'N'S'C', is larger than the original pentagon, WFNSC.

Therefore, the correct statement is a. Pentagon W'F'N'S'C' is larger than pentagon WFNSC because the scale factor is greater than 1.