When you dilate a figure with a scale factor of 1/2, what will the dilated figure look like?
a: The dilated figure will have side lengths that are half the length of the original side lengths. b: The angles in the dilated figure will be half the measure of the original figure. c: The dilated figure will have side lengths twice the length of the original.

Question

01-02-2019
Mathematics

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When you dilate a figure with a scale factor of 1/2, what will the dilated figure look like?
a: The dilated figure will have side lengths that are half the length of the original side lengths. b: The angles in the dilated figure will be half the measure of the original figure. c: The dilated figure will have side lengths twice the length of the original.

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ColinJacobus ColinJacobus · Answer 1 · 2019-02-11T08:10:12+01:00

Answer: The answer is (a). The dilated figure will have side lengths that are half the length of the original side lengths.

Step-by-step explanation: We are asked what the dilated figure will look like after a dilation of scale factor half.

Since the scale factor is half, so the ratio of the area of dilate figure (A) to the area of original figure (a) will be 1 : 2.

That is,

[tex]a : A=1:2\\\\\Rightarrow \dfrac{a}{A}=\dfrac{1}{2}\\\\\\\Rightarrow A=\dfrac{a}{2}.[/tex]

Therefore, the area of the new figure will be half the area of the original one. This gives that each side of the new figure will be half the side of the original figure.

Thus, the correct option is (a).