Chapter 12, Problem 19CT

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.

Answer to Problem 19CT

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

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: ${90}^{\circ }$ counter clockwise rotation.

Graph :

The graph is of $△ABC$

Concept used: In rotation, a figure is turned about the origin through a given angle and direction.

${90}^{\circ }$ Counterclockwise rotation: $\left(x,y\right)\to \left(-y,x\right)$

Let, after the ${90}^{\circ }$ Counterclockwise rotation the new points for A, B and C will be $A^{\prime }$ , $B^{\prime }$ and $C^{\prime }$

Therefore,

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

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

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