Question

the trapezoid ( klmn ) is a dilation of the trapezoid ( klmn ). 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 \(LM\) and \(L'M'\).
The \(y -\) coordinate of \(L\) is \(10\) and of \(M\) is \(0\) (since \(M=(4,0)\)), so \(LM = 10\).
The \(y -\) coordinate of \(L'\) is \(8\) and of \(M'\) is \(0\) (since \(M'=(2,0)\)), so \(L'M'=8\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
So, \(k = \frac{L'M'}{LM}\).
Substitute \(L'M' = 8\) and \(LM = 10\) into the formula: \(k=\frac{8}{10}\).
Simplify \(\frac{8}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\). So, \(k=\frac{4}{5}\).

Answer:

$\frac{4}{5}$