Question

the parallelogram ( mnop ) is a dilation of the parallelogram ( mnop ). 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 side in the original parallelogram

In parallelogram \(MNOP\), the length of \(NO\) (horizontal side). The \(x -\)coordinate of \(N\) is \(0\) and of \(O\) is \(8\). So \(NO=\vert8 - 0\vert=8\).

Step2: Find the length of the corresponding side in the dilated parallelogram

In parallelogram \(M'N'O'P'\), the length of \(N'O'\) (horizontal side). The \(x -\)coordinate of \(N'\) is \(0\) and of \(O'\) is \(2\). So \(N'O'=\vert2 - 0\vert = 2\).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Substitute the values: \(k=\frac{N'O'}{NO}=\frac{2}{8}\).
Simplify the fraction \(\frac{2}{8}=\frac{1}{4}\).

Answer:

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