Question

1. parallelogram ( uvwx ) is a dilation of the parallelogram ( uvwx ). what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a side of the original parallelogram

Take side \(VW\). The coordinates of \(V=(0,3)\) and \(W=(6,3)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same) \(d=\vert x_2 - x_1\vert\), \(VW=\vert6 - 0\vert=6\).

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

Take side \(V'W'\). The coordinates of \(V'=(0,5)\) and \(W'=(9,5)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same) \(d=\vert x_2 - x_1\vert\), \(V'W'=\vert9 - 0\vert = 9\).

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 \(k=\frac{V'W'}{VW}=\frac{9}{6}=\frac{3}{2}\).

Answer:

The scale factor of the dilation is \(\frac{3}{2}\)