Question

the parallelogram ( lmno ) is a dilation of the parallelogram ( lmno ). 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 side \(OL\) of parallelogram \(LMNO\). The \(x -\)coordinate of \(O\) is \(0\) and of \(L\) is \(8\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(OL=\vert8 - 0\vert=8\).

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

Take side \(O'L'\) of parallelogram \(L'M'N'O'\). The \(x -\)coordinate of \(O'\) is \(0\) and of \(L'\) is \(2\). Using the distance formula for horizontal line \(d = \vert x_2 - x_1\vert\), \(O'L'=\vert2 - 0\vert=2\).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k=\frac{O'L'}{OL}\). Substitute \(O'L' = 2\) and \(OL = 8\) into the formula: \(k=\frac{2}{8}=\frac{1}{4}\).

Answer:

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