Question

3. Triangle ABC and triangle A'B'C' are shown below. Triangles NOT to scale.BB1512Why is it certain that triangle A'B'C' is a dilation of triangle ABC?A. Because the areas of the triangles are equal to each other.B. Because triangle ABC and triangle A'B'C' are both triangles.C. Because triangle A'B'C' is a y-axis reflection of triangle ABC.D. Because the side lengths are proportional.

Answer 1

Answer:

D. Because the side lengths are proportional.

Explanation:

Given the attached image;

Triangle ABC and Triangle A'B'C'

Trangle A'B'C' can only be a dilation of Triangle ABC because the side length are proportional.

Dilation of a triangle produces a similar triangle with side length proportional.

$\frac{AB}{A^{\prime}B^{\prime}}=\frac{BC}{B^{\prime}C^{\prime}}=\frac{AC}{A^{\prime}C^{\prime}}$

from the given values;

$\begin{gathered} \frac{AB}{A^{\prime}B^{\prime}}=\frac{4}{12}=\frac{1}{3} \\ \frac{BC}{B^{\prime}C^{\prime}}=\frac{5}{15}=\frac{1}{3} \\ \frac{AC}{A^{\prime}C^{\prime}}=\frac{3}{9}=\frac{1}{3} \end{gathered}$

Therefore, the side lengths are proportional.