Chapter 12.6, Problem 12E

To determine

To graph: the polygon with the vertices and predict the coordinate plane of its image after the rotation, and find the coordinates and draw the image.

  $P\left(-6,2\right),Q\left(-3,4\right),R\left(-1,3\right),S\left(-5,0\right);{90}^{\circ }\text{ clockwise rotation}$

Explanation of Solution

Given : the vertices and rotationprovided in the question,

  $P\left(-6,2\right),Q\left(-3,4\right),R\left(-1,3\right),S\left(-5,0\right);{90}^{\circ }\text{ clockwise rotation}$

Graph:

Interpretation : in ${90}^{\circ }$ clockwise rotation switch the coordinates and multiply the image y -coordinate by -1.

Original

image

  $\begin{array}{l}\left(x,y\right)\to \left(y,-x\right)\\ P\left(-6,2\right)\to A\left(2,6\right)\\ Q\left(-3,4\right)\to B\left(4,3\right)\\ R\left(-1,3\right)\to C\left(3,1\right)\\ S\left(-5,0\right)\to D\left(0,5\right)\end{array}$

So the image lies in the first coordinate.