Chapter 9.5, Problem 55SPR

To determine

To graph $△JKL$ and its image after the indicated transformation.

Answer to Problem 55SPR

  $J^{"}(-6,-4),K^{\text{'}\text{'}}(-4,0),L^{\text{'}\text{'}}(-2,-6)$

Explanation of Solution

Given:

The vertices of $△JKL$ are $J(1,5),K(3,1)$ and .

Translation along $(-7,-1)$ .

Reflection along x-axis.

Calculation:

Translating along the vector $(-7,-1)$ moves triangle left $7$ and down $1$ .

  $(x,y)\to (x-7,y-1)$

  $\begin{array}{l}J(1,5)\to J^{\text{'}}(-6,4)\\ K(3,1)\to K^{\text{'}}(-4,0)\\ L(5,7)\to L^{\text{'}}(-2,6)\end{array}$

Now, trying the reflection in the x-axis:

  $(x,y)\to (x,-y)$

  $\begin{array}{l}{J}^{\text{'}}(-6,4)\to J^{"}(-6,-4)\\ K^{\text{'}}(-4,0)\to K^{\text{'}\text{'}}(-4,0\\ L^{\text{'}}(-2,6)\to L^{\text{'}\text{'}}(-2,-6)\end{array}$

The following is the figure of transformed triangle-