Question

the parallelogram ( efgh ) is a dilation of the parallelogram ( efgh ). 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: Find the length of a corresponding side in both parallelograms

Take the vertical side from \(E\) to \(H\) in parallelogram \(EFGH\). The \(y\) - coordinate of \(E=(1,2)\) and \(H=(1,0)\), so the length \(EH = 2-0=2\).
Take the vertical side from \(E'\) to \(H'\) in parallelogram \(E'F'G'H'\). The \(y\) - coordinate of \(E'=(4,8)\) and \(H'=(4,4)\), so the length \(E'H'=8 - 4=4\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\).
Using the lengths from Step 1: \(k=\frac{E'H'}{EH}\). Substitute \(E'H' = 4\) and \(EH=2\) into the formula, we get \(k=\frac{4}{2}=2\).

Answer:

\(2\)