Question

the rectangle ( vwxy ) is a dilation of the rectangle ( vwxy ). what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a side in the original rectangle

Let's consider the side \(VW\). The \(x\) - coordinate of \(V\) is \(10\) and the \(x\) - coordinate of \(W\) is \(- 6\). Using the distance formula for a horizontal line \(d=\vert x_2 - x_1\vert\), \(VW=\vert10-(-6)\vert=\vert10 + 6\vert = 16\).

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

Consider the side \(V'W'\). The \(x\) - coordinate of \(V'\) is \(8\) and the \(x\) - coordinate of \(W'\) is \(-4\). Using the distance formula for a horizontal line \(d=\vert x_2 - x_1\vert\), \(V'W'=\vert8-(-4)\vert=\vert8 + 4\vert=12\).

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 \(k=\frac{V'W'}{VW}=\frac{12}{16}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)