Chapter 11.4, Problem 2GP

To determine

To graph the $\Delta LMN$ and its image over $x-\text{axis}$ .

Explanation of Solution

Given:

  $\Delta LMN$ with $L(2,1),M(5,2),N(-1,4)$

Calculation for graph:

Let the image of $\Delta LMN$ be $\Delta L\text{'}M\text{'}N\text{'}.$

The image formed by the $\Delta LMN$ can be represented as,

  

Now, graphing out the mirror image.

The mirror image of above triangle will be same but the sign of the coordinates will be changed.

Now, find the coordinates of mirror image by observing the graph.

Coordinates of $\Delta LMN$	Coordinates of $\Delta L\text{'}M\text{'}N\text{'}$
$L(2,1)$	$L\text{'}(2,-1)$
$M(5,2)$	$M\text{'}(5,-2)$
N(-1,4)	$N\text{'}(-1,-4)$

Graph:

  

Interpretation:

In the above graph, the shaded portion shows $\Delta L\text{'}M\text{'}N\text{'}$ .