Chapter 9.4, Problem 34PPS

To determine

To find: The transformation that is required to combine to map the each figure.

Answer to Problem 34PPS

The required transformation in the y axis are $\langle x,y\rangle =\langle x-1,y-6\rangle$ and in the x axis are $\langle x,y\rangle =\langle -x,y\rangle$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the transformation are,

  $\begin{array}{l}J\left(2,2\right)\to J^{\prime }\left(1,-4\right)\\ K\left(3,5\right)\to K^{\prime }\left(2,-1\right)\\ K\left(6,2\right)\to L^{\prime }\left(5,-4\right)\end{array}$

From the above transformation the x translations are,

  $5-6=-1$

The y translations are,

  $-4-2=-6$

Thus, the transformation is described as,

  $\langle x,y\rangle =\langle x-1,y-6\rangle$

The next step is to reflect the JKL in y axis and describe the transformation as,

  $\begin{array}{l}{J}^{\prime }\left(1,-4\right)\to J^{″}\left(-1,-4\right)\\ K\left(2,-1\right)\to K^{″}\left(-2,-1\right)\\ K\left(5,-4\right)\to L^{″}\left(-5,-4\right)\end{array}$

Thus, the transformation is described as,

  $\langle x,y\rangle =\langle -x,y\rangle$

Thus, the required transformation in the y axis are $\langle x,y\rangle =\langle x-1,y-6\rangle$ and in the x axis are $\langle x,y\rangle =\langle -x,y\rangle$ .