Chapter 12, Problem 23CR

To determine

To draw : A $△ABC$ with vertices $A\left(-4,1\right)$ , $B\left(-2,3\right)$ and $C\left(-1,1\right)$ . Find the coordinates of the vertices of the image after the specified translation and draw the image.

Explanation of Solution

Given information : Coordinates of the vertices $△ABC$ are $A\left(-4,1\right)$ , $B\left(-2,3\right)$ and $C\left(-1,1\right)$ .

The specified translation rule is $\left(x,y\right)\to \left(x-3,y-4\right)$ .

Graph :

The specified translation rule is $\left(x,y\right)\to \left(x-3,y-4\right)$ .

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

Therefore,

  $\begin{array}{l}A\left(-4,1\right)\to \left(-4-3,1-4\right)=A^{\prime }\left(-7,-3\right)\\ B\left(-2,3\right)\to \left(-2-3,3-4\right)=B^{\prime }\left(-5,-1\right)\\ C\left(-1,1\right)\to \left(-1-3,1-4\right)=C^{\prime }\left(-4,-3\right)\end{array}$

The coordinates of the vertices of the image after specified translation are $A^{\prime }\left(-7,-3\right)$ , $B^{\prime }\left(-5,-1\right)$ , $C^{\prime }\left(-4,-3\right)$ .

Interpretation : The coordinates of the vertices of the image after specified translation are $A^{\prime }\left(-7,-3\right)$ , $B^{\prime }\left(-5,-1\right)$ , $C^{\prime }\left(-4,-3\right)$ .