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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). Select the correct statement. A. The slope of W'X' is , and the length of W'X' is 5. B. The slope of W'X' is , and the length of W'X' is 15. C. The slope of W'X' is , and the length of W'X' is 15. D. The slope of W'X' is , and the length of W'X' is 5.

Sagot :

Martebi

Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

What is the vertex about?

The coordinates in the question were:

(3,2), and  (7,5).

Then the slope of WX is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

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

    =3/4

The length of WX is calculated by:

[tex]WX = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1}) ^ 2}[/tex]

[tex]\sqrt{(7-3)^2 + (5-2)^2} \\\\= \sqrt{25} \\\\= 5[/tex]

Since, The scale factor is  =  3.

Hence, WX = 3 x 5 = 15

Therefore, Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

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