Question

the parallelogram ( tuvw ) is a dilation of the parallelogram ( tuvw ). what is the scale factor 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 corresponding sides

Let's consider the vertical side of the parallelograms. For parallelogram \(TUVW\), the vertical side (e.g., from \(U(1,1)\) to \(V(1, - 1)\)) has a length of \(|1-(-1)| = 2\). For parallelogram \(T'U'V'W'\), the vertical side (e.g., from \(U'(5,5)\) to \(V'(5,-5)\)) has a length of \(|5 - (-5)|=10\).

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 lengths from Step 1, \(k=\frac{10}{2}=5\).

Answer:

\(5\)