Question

the parallelogram ( bcde ) is a dilation of the parallelogram ( bcde ). 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 of the original parallelogram

Take the vertical side \(BE\) of parallelogram \(BCDE\). The \(y -\)coordinate of \(B\) is \(10\) and the \(y -\)coordinate of \(E\) is \(5\). So the length of \(BE=10 - 5=5\)

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

Take the vertical side \(B'E'\) of parallelogram \(B'C'D'E'\). The \(y -\)coordinate of \(B'\) is \(2\) and the \(y -\)coordinate of \(E'\) is \(1\). So the length of \(B'E'=2 - 1 = 1\)

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of a side of the image}}{\text{length of the corresponding side of the pre - image}}\). So \(k=\frac{B'E'}{BE}=\frac{1}{5}\)

Answer:

$\frac{1}{5}$