Question

find the scale factor of triangle abc if it is dilated to triangle abc. type your result in the empty box below.

Explanation:

Step1: Identify lengths of corresponding sides

Let's assume the grid has each square with side length 1. For triangle \( ABC \) and \( A'B'C' \), let's take the base (along the x - axis) and the height (along the y - axis).
For triangle \( ABC \), let's say the length of \( BC \) (base) is, from the graph, let's count the grids. Suppose \( BC = 4 \) units and \( AC \) (height) is \( 6 \) units (just for example, we can also take the ratio of corresponding sides). For triangle \( A'B'C' \), the length of \( B'C' \) (base) is \( 2 \) units and \( A'C' \) (height) is \( 3 \) units.

Step2: Calculate the scale factor

The scale factor \( k \) of a dilation from a figure to its image is given by the ratio of the length of a side of the image (\( A'B'C' \)) to the length of the corresponding side of the original figure (\( ABC \)).
So, if we take the base \( B'C' \) and \( BC \), let \( BC = x \) and \( B'C'=y \). From the graph, let's count the number of grid squares. Let's assume \( BC = 4 \) (from \( C \) to \( B \)) and \( B'C' = 2 \) (from \( C \) to \( B' \)). Then the scale factor \( k=\frac{B'C'}{BC}=\frac{2}{4}=\frac{1}{2} \). (We can also check with the height: if \( AC = 6 \) and \( A'C' = 3 \), then \( \frac{A'C'}{AC}=\frac{3}{6}=\frac{1}{2} \))

Answer:

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