Chapter 14.5, Problem 5ST1

To determine

To choose the correct answer.

Answer to Problem 5ST1

A) $\overline{AB}\parallel \overline{A\text{'}B\text{'}}$ and B) $\frac{A\text{'}B\text{'}}{AB}=3$

Explanation of Solution

Given information:

The given statement is:

“A dilation with scale factor $3$ maps $\Delta ABC$ to $\Delta A\text{'}B\text{'}C\text{'}$ . Which of the following are true?”

A) $\overline{AB}\parallel \overline{A\text{'}B\text{'}}$

B) $\frac{A\text{'}B\text{'}}{AB}=3$

C) $\frac{\text{area of }\Delta A\text{'}B\text{'}C\text{'}}{\text{area of }\Delta ABC}=3$

On dilation, the corresponding sides are parallel.

The ratio of the sides is equal to the scale factor.

The ratio of the areas are equal to the square of the scale factor.

Hence, the statements A) $\overline{AB}\parallel \overline{A\text{'}B\text{'}}$ and B) $\frac{A\text{'}B\text{'}}{AB}=3$ are true and the statement C) $\frac{\text{area of }\Delta A\text{'}B\text{'}C\text{'}}{\text{area of }\Delta ABC}=3$ is false.