Question

the trapezoid ( fghi ) is a dilation of the trapezoid ( fghi ). 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

Let's take side \(HI\) and \(H'I'\).
The \(y -\)coordinate of \(H\) is \(6\) and of \(I\) is \(6\), so \(HI\) has a length of \(4 - (- 4)=8\) (using the \(x -\)coordinates of \(H(-4,6)\) and \(I(4,6)\)).
The \(y -\)coordinate of \(H'\) is \(8\) and of \(I'\) is \(8\), so \(H'I'\) has a length of \(6-(-4) = 10\) (using the \(x -\)coordinates of \(H'(-4,8)\) and \(I'(6,8)\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of the image side}}{\text{length of the original side}}\).
\(k=\frac{H'I'}{HI}\)
Substitute \(H'I' = 10\) and \(HI = 8\) into the formula: \(k=\frac{10}{8}=\frac{5}{4}\)

Answer:

\(\frac{5}{4}\)