Question

error analysis for the dilation with center (0,0) shown on the graph, your friend says the scale factor is $\frac{8}{3}$. what is the correct scale factor? what mistake did your friend likely make? the correct scale factor is 8 what mistake did your friend likely make? a. your friend found the ratio between two sides of the original triangle. b. your friend found the scale factor that enlarges $\triangle abc$ to $\triangle abc$. c. your friend found the ratio between non - corresponding sides. d. your friend found the ratio between two sides of the image triangle.

Explanation:

Step1: Identify dilation direction

From the graph, $\triangle A'B'C'$ is smaller than $\triangle ABC$, so the scale factor is the ratio of image side length to original side length, less than 1.

Step2: Calculate correct scale factor

The friend gave $\frac{6}{3}=2$, which is enlarging. The correct factor is $\frac{\text{Image length}}{\text{Original length}}=\frac{3}{6}=\frac{1}{2}$.

Step3: Analyze friend's mistake

The friend used original length over image length, which is the scale factor to enlarge the image back to the original triangle.

Answer:

The correct scale factor is $\boldsymbol{\frac{1}{2}}$
B. Your friend found the scale factor that enlarges $\Delta A'B'C'$ to $\Delta ABC$.