Question

polygon wxyz is dilated by a scale factor of 3 with vertex w as the center of dilation, resulting in polygon wxyz. the coordinates of point w are (3,2), and the coordinates of point x are (7,5). select the correct statement. a. the slope of \\(\overline{wx}\\) is \\(\frac{3}{4}\\), and the length of \\(\overline{wx}\\) is 5. b. the slope of \\(\overline{wx}\\) is \\(\frac{9}{4}\\), and the length of \\(\overline{wx}\\) is 5. c. the slope of \\(\overline{wx}\\) is \\(\frac{3}{4}\\), and the length of \\(\overline{wx}\\) is 15. d. the slope of \\(\overline{wx}\\) is \\(\frac{9}{4}\\), and the length of \\(\overline{wx}\\) is 15.

Explanation:

Step1: Calculate slope of WX

Slope formula: $\frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{7 - 3} = \frac{3}{4}$. Dilation preserves slope, so slope of WX' is $\frac{3}{4}$.

Step2: Calculate length of WX

Distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(7-3)^2 + (5-2)^2} = \sqrt{16 + 9} = 5$.

Step3: Find length of WX'

Scale factor 3: $5 \times 3 = 15$.

Answer:

C. The slope of $\overline{WX'}$ is $\frac{3}{4}$, and the length of $\overline{WX'}$ is 15.