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Rectangle ABCD has vertices A(4, 8), B(8, 8) , C(8, −4) and D(4, −4) . The rectangle is dilated by a scale factor of 3/4 , with the origin as the center of dilation. What are the coordinates of the vertices in the image? Enter your answers in the boxes.

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Answer:

A'(3, 6)

B'(6, 6)

C'(6, -3)

D'(3, -3)

Step-by-step explanation:

To find the image of a geometric figure after a dilation centered at the origin, you just need to multiply each vertex of the geometric figure by the scale factor.

We know that the scale factor is [tex]\frac{3}{4}[/tex], so let's multiply each vertex by it:

[tex]A=(4, 8)[/tex], so

[tex]A'=\frac{3}{4} (4,8)=(\frac{3}{4} *4,\frac{3}{4} *8)=(3,6)[/tex]

[tex]B=(8,8)[/tex]

[tex]B'=(\frac{3}{4} *8,\frac{3}{4} *8)=(6,6)[/tex]

[tex]C=(8,-4)[/tex]

[tex]C'=(\frac{3}{4} *8,\frac{3}{4} *-4)=(6, -3)[/tex]

[tex]D=(4,-4)[/tex]

[tex]D'=(\frac{3}{4} *4,\frac{3}{4} *-4)=(3,-3)[/tex]

We can conclude that the vertices of the image are A'(3, 6), B'(6, 6), C'(6, -3), and D'(3, -3)

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