Question

the trapezoid abcd is a dilation of the trapezoid abcd. 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

Let's consider the vertical side \(AB\) and \(A'B'\).
The coordinates of \(A=( - 4,0)\) and \(B=(8,3)\), but for the vertical side, if we consider the vertical distance from \(A\) to \(D\) (since \(AD\) is vertical). \(A=( - 4,0)\) and \(D=( - 4,3)\), so \(AD = 3\) units.
The coordinates of \(A'=( - 1,0)\) and \(D'=( - 1,1)\), so \(A'D'=1\) unit.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\)
\(k = \frac{A'D'}{AD}\)
Since \(A'D' = 1\) and \(AD=3\), \(k=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)