Question

the parallelogram ( hijk ) is a dilation of the parallelogram ( hijk ). 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: Identify corresponding side lengths

Find the length of a side in the original parallelogram \(HIJK\) and the corresponding side in the dilated parallelogram \(H'I'J'K'\).
For example, consider the horizontal sides. In parallelogram \(HIJK\), if we assume \(IJ\) (from \(x = 4\) to \(x = 8\)), the length \(IJ=8 - 4=4\). In parallelogram \(H'I'J'K'\), \(I'J'\) (from \(x = 1\) to \(x = 2\)), the length \(I'J'=2 - 1 = 1\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Using the side lengths from Step 1: \(k=\frac{I'J'}{IJ}\). Substitute \(I'J' = 1\) and \(IJ = 4\) into the formula. So \(k=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)