In a dilation, the image is similar to the preimage. If the scale factor is k, what happens to lengths and areas?

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Multiple Choice

In a dilation, the image is similar to the preimage. If the scale factor is k, what happens to lengths and areas?

Explanation:
In a dilation, all linear dimensions scale by the factor k, so every length multiplies by k. Areas scale by the square of that factor because area is a two-dimensional measure: when you scale both dimensions by k, the new area is (k times original length) times (k times original width), which gives k^2 times the original area. For example, a rectangle with area ab becomes a new rectangle with sides ka and kb, whose area is (ka)(kb) = k^2ab. So lengths are multiplied by k and areas by k^2.

In a dilation, all linear dimensions scale by the factor k, so every length multiplies by k. Areas scale by the square of that factor because area is a two-dimensional measure: when you scale both dimensions by k, the new area is (k times original length) times (k times original width), which gives k^2 times the original area. For example, a rectangle with area ab becomes a new rectangle with sides ka and kb, whose area is (ka)(kb) = k^2ab. So lengths are multiplied by k and areas by k^2.

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