Question

the parallelogram ( qrst ) is a dilation of the parallelogram ( qrst ). 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

In parallelogram \(QRST\), let's consider the vertical distance from \(R(1,9)\) to \(Q(8,9)\) (horizontal side). The length of \(RQ\) is \(8 - 1=7\) units.
In parallelogram \(Q'R'S'T'\), the vertical distance from \(R'(0,3)\) to \(Q'(2,3)\) (horizontal side). The length of \(R'Q'\) is \(2-0 = 2\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
\(k=\frac{2}{7}\)

Answer:

\(\frac{2}{7}\)