Chapter 12, Problem 18CT

To determine

To draw : A $△ABC$ with vertices $A\left(-3,4\right)$ , $B\left(-2,5\right)$ and $C\left(-1,3\right)$ . 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 $△ABC$ are $A\left(-3,4\right)$ , $B\left(-2,5\right)$ and $C\left(-1,3\right)$ .

Type of transformation: Reflection in the axis.

Graph :

  

The graph is of $△ABC$

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 the new points for A, B and C will be $A^{\prime }$ , $B^{\prime }$ and $C^{\prime }$

Therefore,

  $\begin{array}{l}A\left(-3,4\right)\to \left(-3,-4\right)=A^{\prime }\left(-3,-4\right)\\ B\left(-2,5\right)\to \left(-2,-5\right)=B^{\prime }\left(-2,-5\right)\\ C\left(-1,3\right)\to \left(-1,-3\right)=C^{\prime }\left(-1,-3\right)\end{array}$

The coordinates of the vertices of the image after specified transformation are $A^{\prime }\left(-3,-4\right)$ , $B^{\prime }\left(-2,-5\right)$ , $C^{\prime }\left(-1,-3\right)$ .

  

Interpretation : The coordinates of the vertices of the image after specified transformation are $A^{\prime }\left(1,-3\right)$ , $B^{\prime }\left(2,-2\right)$ , $C^{\prime }\left(3,-4\right)$ .