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Quadrilateral WXYZ with vertices W(0,-4), X(13,0), Y(9,-12), and Z(5,-12); scale factor: k = 3/4, center of dilation: (1,0).
W’
X’
Y’
Z’

Sagot :

MrRoyal

Dilation involves changing the size of a quadrilateral or any shape

The coordinates of the image of the dilation are: [tex]W' = (1/4,-3)[/tex], [tex]X' = (10,0)[/tex], [tex]Y' = (7,-9)[/tex] and [tex]Z' = (4,-9)[/tex]

How to determine the vertices of the image

The vertices of the pre-image are given as:

W = (0,-4)

X = (13,0)

Y = (9,-12)

Z = (5,-12)

The scale factor is given as:

k = 3/4

The center of dilation is given as:

(a,b) = (1,0)

To calculate the vertices of the image, we make use of the following formula

[tex](x'y') = (k(x-a) + a,k(y-b) + b)[/tex]

So, we have:

[tex]W' = (3/4(0-1) + 1,3/4(-4-0) + 0)[/tex]

[tex]W' = (1/4,-3)[/tex]

[tex]X' = (3/4(13-1) + 1,3/4(0-0) + 0)[/tex]

[tex]X' = (10,0)[/tex]

[tex]Y' = (3/4(9-1) + 1,3/4(-12-0) + 0)[/tex]

[tex]Y' = (7,-9)[/tex]

[tex]Z' = (3/4(5-1) + 1,3/4(-12-0) + 0)[/tex]

[tex]Z' = (4,-9)[/tex]

Hence, the coordinates of the image of the dilation are:

[tex]W' = (1/4,-3)[/tex], [tex]X' = (10,0)[/tex], [tex]Y' = (7,-9)[/tex] and [tex]Z' = (4,-9)[/tex]

Read more about dilation at:

https://brainly.com/question/10253650

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