Question

1
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 15.
b. the slope of $overline{wx}$ is $\frac{3}{4}$, and the length of $overline{wx}$ is 5.
c. the slope of $overline{wx}$ is $\frac{4}{3}$, and the length of $overline{wx}$ is 15.
d. the slope of $overline{wx}$ is $\frac{3}{4}$, and the length of $overline{wx}$ is 5.

Explanation:

Step1: Calculate slope of $\overline{WX}$

Slope formula: $\frac{y_2-y_1}{x_2-x_1} = \frac{5-2}{7-3} = \frac{3}{4}$

Step2: Find length of $\overline{WX}$

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

Step3: Scale length for $\overline{W'X'}$

Scaled length: $5 \times 3 = 15$

Step4: Note slope invariance under dilation

Slope of $\overline{W'X'}$ = $\frac{3}{4}$

Answer:

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