Question

xyz is a scale copy of
abc.
what is the scale factor?

Explanation:

Step1: Determine lengths of corresponding sides

Assume each grid square has side length 1. For triangle \(ABC\), let's find the length of \(AB\). From the grid, \(AB\) spans 2 units (e.g., from \(A\) to \(B\) horizontally, 2 squares). For triangle \(XYZ\), \(XY\) spans 6 units (from \(X\) to \(Y\) horizontally, 6 squares).

Step2: Calculate scale factor

Scale factor is the ratio of length of corresponding side in image (\(XYZ\)) to pre - image (\(ABC\)). So scale factor \(=\frac{XY}{AB}=\frac{6}{2} = 3\). We can also check with the vertical sides. Let \(BC\) be the vertical side of \(ABC\), say it's 2 units (2 squares), and \(YZ\) be the vertical side of \(XYZ\), say it's 6 units (6 squares). Then \(\frac{YZ}{BC}=\frac{6}{2}=3\), confirming the scale factor.

Answer:

3