Chapter 4, Problem 7STP

To determine

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

Answer to Problem 7STP

The correct option is option A

Explanation of Solution

Given:

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

The vertices of the triangle after the dilation is $A\text{'}\left(-12,6\right),B\text{'}\left(-12,-9\right),C\text{'}\left(9,-6\right)$

Calculation:

Consider the vertices of $A$ is,

  $A\left(-4,2\right)$

Consider the vertices of $A^{\prime }$ is,

  $A^{\prime }\left(-4,2\right)$

Consider the dilation matrix of the matrix $A$ is,

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

Thus, the perimeter of $\Delta A\text{'}B\text{'}C\text{'}$ 3 times that of $ABC$ .