Question

identify the scale factor used to graph the image below. k =____

Explanation:

Step1: Find the length of a side in the original figure and its corresponding side in the image

Let's consider the horizontal distance from \(H\) to \(I\) in the original triangle and from \(H'\) to \(I'\) in the image triangle.
Suppose the distance from \(H\) to \(I\) (original) is \(2\) units (counting the grid - squares). The distance from \(H'\) to \(I'\) (image) is \(6\) units.

Step2: Calculate the scale factor \(k\)

The scale factor \(k=\frac{\text{length of side in image}}{\text{length of side in original}}\).
Using the formula \(k = \frac{HI'}{HI}\), substituting \(HI'=6\) and \(HI = 2\), we get \(k=\frac{6}{2}=3\).

Answer:

\(k = 3\)