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Rectangle ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?

A′

B′

C′

D′

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Rectangle ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?

A′ (8×1.2=9.6,5×1.2=6)

The term "dilation" refers to a transformation that is used to downsize an item. The vertex in the dilated image that has coordinates of (9.6, 6) is A'.

What is dilation?

The term "dilation" refers to a transformation that is used to downsize an item. Dilation is a technique for making items appear bigger or smaller. The picture produced by this transformation is identical to the original shape.

As it is given that the Rectangle ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5). with a scale factor of 1.2, therefore, the vertexes of the dilated rectangle can be written as,

[tex]A' = (8 \times 1.2,\ 5 \times 1.2) = (9.6,6)[/tex]

[tex]B' = (8 \times 1.2,\ 10 \times 1.2) = (9.6,12)[/tex]

[tex]C' = (14 \times 1.2,\ 10 \times 1.2) = (16.8, 12)[/tex]

[tex]D' = (14 \times 1.2,\ 5 \times 1.2) = (16.8, 6)[/tex]

Hence, the vertex in the dilated image that has coordinates of (9.6, 6) is A'.

Learn more about Dilation:

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