Question

the trapezoid ( vwxy ) is a dilation of the trapezoid ( vwxy ). 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 in both trapezoids

In trapezoid \(VWXY\), let's consider the side \(WX\). The \(y -\)coordinate of \(W\) and \(X\) is \(5\). The \(x -\)coordinates of \(W=- 5\) and \(X = 0\). Using the distance formula for a horizontal line \(d=\vert x_2 - x_1\vert\), the length of \(WX=\vert0-(-5)\vert = 5\).
In trapezoid \(V'W'X'Y'\), consider the corresponding side \(W'X'\). The \(y -\)coordinate of \(W'\) and \(X'\) is \(2\). The \(x -\)coordinates of \(W'=-2\) and \(X'=0\). Using the distance formula for a horizontal line \(d = \vert x_2 - x_1\vert\), the length of \(W'X'=\vert0 - (-2)\vert=2\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Substituting the values we found: \(k=\frac{W'X'}{WX}\).
Since \(W'X' = 2\) and \(WX = 5\), then \(k=\frac{2}{5}\).

Answer:

\(\frac{2}{5}\)