Question

1. draw the dilation of abcd by a scale factor of \\(\frac{1}{2}\\). what is the ratio of the perimeter of the dilated quadrilateral to the perimeter of the original quadrilateral?
2. draw the dilation of \\(\triangle def\\) by a scale factor of 2. what is the ratio of the area of the dilated triangle to the area of the original triangle?

Explanation:

Problem 7

Step1: Recall perimeter dilation rule

For a dilation with scale factor $k$, the ratio of perimeters of dilated to original figure equals $k$.

Step2: Identify given scale factor

The scale factor $k = \frac{1}{2}$.

Step1: Recall area dilation rule

For a dilation with scale factor $k$, the ratio of areas of dilated to original figure equals $k^2$.

Step2: Identify given scale factor

The scale factor $k = 2$.

Step3: Calculate the area ratio

$k^2 = 2^2 = 4$

Answer:

$\frac{1}{2}$

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Problem 8