Question

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

Let's consider the vertical side from \(N\) to \(Q\) in parallelogram \(NOPQ\) and from \(N'\) to \(Q'\) in parallelogram \(N'O'P'Q'\).
The \(y -\)coordinate of \(N\) is \(3\) and of \(Q\) is \(- 2\). So the length \(NQ=\vert3-(-2)\vert = 5\).
The \(y -\)coordinate of \(N'\) is \(5\) and of \(Q'\) is \(-5\). So the length \(N'Q'=\vert5 - (- 5)\vert=10\).

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 lengths from Step 1: \(k=\frac{N'Q'}{NQ}\).
Substitute \(N'Q' = 10\) and \(NQ = 5\) into the formula: \(k=\frac{10}{5}\).

Answer:

\(2\)