Question

what scale factor was used to produce the image?

Explanation:

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

Original triangle: side from \((1,1)\) to \((1,6)\) has length \(6 - 1=5\).
Image triangle: side from \((1,1)\) to \((3,1)\) has length \(3 - 1 = 2\). Wait, no, better use another approach. Let's assume the original triangle has vertices \((1,6)\), \((1,1)\), \((9,1)\). The image has vertices \((1,1)\), \((3,1)\), \((1,3)\).
Original horizontal side: from \((1,1)\) to \((9,1)\) length \(9 - 1=8\).
Image horizontal side: from \((1,1)\) to \((3,1)\) length \(3 - 1 = 2\).

Step2: Calculate the scale factor

Scale factor \(k=\frac{\text{length of image side}}{\text{length of original side}}\).
\(k=\frac{2}{4}=\frac{1}{2}\) (assuming original side from \((1,1)\) to \((5,1)\) (length \(4\)) and image side from \((1,1)\) to \((3,1)\) (length \(2\)) after re - evaluating the graph (counting grid units: original base spans \(4\) units (e.g., from \(x = 1\) to \(x=5\)), image base spans \(2\) units (from \(x = 1\) to \(x = 3\))).

Answer:

\(\frac{1}{2}\)