Question

the triangle cde is a dilation of the triangle cde. 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 triangles

Let's consider the vertical side. For triangle \(CDE\), the vertical side from \(C(-4,4)\) to \(E(-4,-8)\). The length is \(4 - (-8)=12\). For triangle \(C'D'E'\), the vertical side from \(C'(-5,5)\) to \(E'(-5,-10)\). The length is \(5-(-10) = 15\).

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 \(k=\frac{15}{12}\). Simplifying \(\frac{15}{12}=\frac{5}{4}\)

Answer:

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