Question

the triangle ( ghi ) is a dilation of the triangle ( ghi ). 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 coordinates of corresponding points

Let's assume \(H(-9,-7)\) and \(H'(-3,-2)\). But it's easier to use vertical or horizontal segments. For example, consider the vertical segment from \(G(-9,-9)\) to \(H(-9,-4)\), its length is \(|-4 - (-9)|=5\). The corresponding vertical segment from \(G'(-3,-3)\) to \(H'(-3,-2)\), its length is \(|-2-(-3)| = 1\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a segment in the image to the length of the corresponding segment in the pre - image. So \(k=\frac{\text{length of segment in image}}{\text{length of segment in pre - image}}\). Using the vertical segments: \(k=\frac{1}{5}\)

Answer:

\(\frac{1}{5}\)