Question

Polygon WXYZ is dilated by a scale factor of 3 with vertex W as the center of dilation, resulting in polygon W’X’Y’Z’. The coordinates of point w
are (3,2), and the coordinates of point X are (7,5).

Answer 1

Dilating polygon WXYZ will change the side lengths of the polygon

The true statement is (b) the slope of WX is 3/4, and the length of W'X' is 15

The coordinates are given as:

$\mathbf{W = (3,2)}$

$\mathbf{X = (7,5)}$

The slope of WX is:

$\mathbf{m =\frac{y_2 - y_1}{x_2 -x_1}}$

So, we have:

$\mathbf{m =\frac{5-2}{7-3}}$

$\mathbf{m =\frac{3}{4}}$

The length of WX is calculated using:

$\mathbf{WX = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

So, we have:

$\mathbf{WX = \sqrt{(7- 3)^2 + (5- 2)^2}}$

$\mathbf{WX = \sqrt{25}}$

$\mathbf{WX = 5}$

The scale factor is 3.

So, the distance W'X' is:

$\mathbf{W'X' = 3 \times WX}$

This gives

$\mathbf{W'X' = 3 \times 5}$

$\mathbf{W'X' = 15}$

Hence, the true statement is (b)

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