Question

the parallelogram bcde is a dilation of the parallelogram bcde. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Select corresponding side lengths

Choose a side of the original parallelogram BCDE and its corresponding side in the dilated parallelogram B'C'D'E'. Let's consider the horizontal side BC and B'C'. The length of BC can be found by calculating the difference in x - coordinates of B and C. B(-4,4) and C(4,4), so the length of BC is \(|4 - (-4)|=8\). B'(-2,2) and C'(2,2), so the length of B'C' is \(|2-(-2)| = 4\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure. So \(k=\frac{\text{length of side in dilated figure}}{\text{length of corresponding side in original figure}}\). Substituting the values of B'C' and BC, we get \(k=\frac{4}{8}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)