Question

error analysis for the dilation with center (0,0) shown on the graph, your friend says the scale factor is \\( \frac{10}{3} \\). what is the correct scale factor? what mistake did your friend likely make? the correct scale factor is \\( \square \\). what mistake did your friend likely make? a. your friend found the ratio between two sides of the image triangle. b. your friend found the ratio between two sides of the original triangle. c. your friend found the scale factor that enlarges \\( \triangle abc \\) to \\( \triangle abc \\). d. your friend found the ratio between non - corresponding sides.

Explanation:

Step1: Identify corresponding points

Original point $A(0,10)$, image $A'(0,3)$; center is $(0,0)$.

Step2: Calculate scale factor

Scale factor $k = \frac{\text{Image coordinate}}{\text{Original coordinate}} = \frac{3}{10}$

Step3: Analyze friend's error

Friend used $\frac{10}{3}$, which is $\frac{\text{Original}}{\text{Image}}$, reversing the ratio (using original over image instead of image over original, i.e., enlarging image to original instead of original to image).

Answer:

The correct scale factor is $\frac{3}{10}$.
C. Your friend found the scale factor that enlarges $\Delta A'B'C'$ to $\Delta ABC$.