Chapter 12, Problem 25CR

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 y-axis.

Graph :

The graph is of $△LMN$

Type of transformation: Reflection in the y axis.

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

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

Let, after the reflection in Y-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 Y-axis are $L^{\prime }\left(3,-1\right)$ , $M^{\prime }\left(2,-2\right)$ , $N^{\prime }\left(4,-3\right)$ .

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