Question

the trapezoid ( tuvw ) is a dilation of the trapezoid ( tuvw ). 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 take side \(TU\) and \(T'U'\).
The length of \(TU\): \(T(2,0)\) and \(U(0,0)\), so \(TU=\vert2 - 0\vert= 2\).
The length of \(T'U'\): \(T'(10,0)\) and \(U'(0,0)\), so \(T'U'=\vert10 - 0\vert = 10\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Using the sides \(TU\) (pre - image) and \(T'U'\) (image), \(k=\frac{T'U'}{TU}\).
Substitute \(T'U' = 10\) and \(TU = 2\) into the formula: \(k=\frac{10}{2}=5\).

Answer:

\(5\)