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 horizontal side \(YX\). The \(y -\)coordinate of \(Y\) is \(3\) and of \(X\) is \(3\) (since \(Y(- 2,3)\) and \(X(2,3)\)). Using the distance formula for horizontal points \(d=\vert x_2 - x_1\vert\), the length of \(YX=\vert2-(-2)\vert = 4\).
In trapezoid \(V'W'X'Y'\), the \(y -\)coordinate of \(Y'\) is \(9\) and of \(X'\) is \(9\) (since \(Y'(-6,9)\) and \(X'(8,9)\)). Using the distance formula for horizontal points \(d=\vert x_2 - x_1\vert\), the length of \(Y'X'=\vert8-(-6)\vert = 14\).

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: \(k = \frac{14}{4}=\frac{7}{2}\)

Answer:

\(\frac{7}{2}\)