Chapter 12, Problem 24CR

To determine

To draw : A $△LMN$ with vertices $L\left(-3,-1\right)$ , $M\left(-2,-2\right)$ and $N\left(-4,-3\right)$ . Find the coordinates of the vertices of the image after the specified transformation and draw the image.

Explanation of Solution

Given information : Coordinates of the vertices of $△LMN$ are $L\left(-3,-1\right)$ , $M\left(-2,-2\right)$ and $N\left(-4,-3\right)$ .

Type of transformation: Reflection in the X-axis.

Graph :

The graph is of $△LMN$

Type of transformation: Reflection in the X axis.

Concept used: In reflection, a figure is flipped over a line.

Reflection in X-axis: $\left(x,y\right)\to \left(x,-y\right)$

Let, after the reflection in X-axis the new points for $L$ , $M$ and $N$ will be $L^{\prime }$ , $M^{\prime }$ and $N^{\prime }$

Therefore,

  $\begin{array}{l}L\left(-3,-1\right)\to \left(-3,-(-1)\right)=L^{\prime }\left(-3,1\right)\\ M\left(-2,-2\right)\to \left(-2,-(-2)\right)=M^{\prime }\left(-2,2\right)\\ N\left(-4,-3\right)\to \left(-4,-(-3)\right)=N^{\prime }\left(-4,3\right)\end{array}$

The coordinates of the vertices of the image after reflection in X-axis are $L^{\prime }\left(-3,1\right)$ , $M^{\prime }\left(-2,2\right)$ , $N^{\prime }\left(-4,3\right)$ .

Interpretation : The coordinates of the vertices of the image after reflection in X-axis are $L^{\prime }\left(-3,1\right)$ , $M^{\prime }\left(-2,2\right)$ , $N^{\prime }\left(-4,3\right)$ .