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).

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MrRoyal MrRoyal · Answer 1 · 2021-11-10T13:26:15+01:00

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:

[tex]\mathbf{W = (3,2)}[/tex]

[tex]\mathbf{X = (7,5)}[/tex]

The slope of WX is:

[tex]\mathbf{m =\frac{y_2 - y_1}{x_2 -x_1}}[/tex]

So, we have:

[tex]\mathbf{m =\frac{5-2}{7-3}}[/tex]

[tex]\mathbf{m =\frac{3}{4}}[/tex]

The length of WX is calculated using:

[tex]\mathbf{WX = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}[/tex]

So, we have:

[tex]\mathbf{WX = \sqrt{(7- 3)^2 + (5- 2)^2}}[/tex]

[tex]\mathbf{WX = \sqrt{25}}[/tex]

[tex]\mathbf{WX = 5}[/tex]

The scale factor is 3.

So, the distance W'X' is:

[tex]\mathbf{W'X' = 3 \times WX}[/tex]

This gives

[tex]\mathbf{W'X' = 3 \times 5}[/tex]

[tex]\mathbf{W'X' = 15}[/tex]

Hence, the true statement is (b)