Chapter 4.4, Problem 52HP

To determine

To find: The number of times the perimeter of $\Delta A\text{'}B\text{'}C\text{'}$ as that of $\Delta ABC$ .

Answer to Problem 52HP

The correct option is A.

Explanation of Solution

Given:

The vertices of the $\Delta ABC$ are $A\left(-4,2\right)$ , $B\left(-4,-3\right)$ and $C\left(3,-2\right)$ .

The vertices of the $\Delta A\text{'}B\text{'}C\text{'}$ are $A\text{'}\left(-12,6\right)$ , $B\text{'}\left(-12,-9\right)$ and $C\text{'}\left(9,-6\right)$ .

Calculation:

Calculate the scalar factor as follows.

  $\begin{array}{c}\left[\begin{array}{c}-4\\ 2\end{array}\right]\left[x\right]=\left[\begin{array}{c}-12\\ 6\end{array}\right]\\ \left[\begin{array}{c}-4x\\ 2x\end{array}\right]=\left[\begin{array}{c}-12\\ 6\end{array}\right]\\ -4x=-12\\ x=3\end{array}$

Therefore, the scalar factor is 3.

Hence, the correct option is A.