Chapter 9.4, Problem 45HP

To determine

To find: The coordinates of $A^{\prime }$ after the transformation.

Answer to Problem 45HP

The correct option is A.

Explanation of Solution

Given:

The given graph is shown in Figure 1

  

Figure 1

Calculation:

Consider the triangle $\Delta ABC$ is translated across the vector $\langle -2,3\rangle$ and then it is reflected in the x axis. Then calculate the coordinates of $A^{″}$ after the transformation.

The coordinates of triangle $\Delta ABC$ along $\langle -2,3\rangle$ as,

  $\begin{array}{l}\left(x,y\right)\to \left(x,-y\right)\\ A^{\prime }\left(1,4\right)\to A^{″}\left(1,-4\right)\end{array}$

Thus, the coordinates of $A^{″}\left(1,-4\right)$ .

The correct option is A.