Question

the triangle ( vwx ) is a dilation of the triangle ( vwx ). 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 corresponding side

Take side \(VX\).
For triangle \(VWX\), \(V(-2,1)\) and \(X(-2,-3)\). Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) (or since \(x\)-coordinates are the same, \(d=\vert y_2 - y_1\vert\)), \(VX=\vert1-(-3)\vert = 4\).
For triangle \(V'W'X'\), \(V'(-6,3)\) and \(X'(-6,-9)\). Using the distance formula (or since \(x\)-coordinates are the same), \(V'X'=\vert3-(-9)\vert = 12\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\).
\(k=\frac{V'X'}{VX}\)
Substitute \(V'X' = 12\) and \(VX = 4\) into the formula: \(k=\frac{12}{4}=3\).

Answer:

\(3\)