Chapter 12.6, Problem 23E

To determine

To graph:the polygon after the ${90}^{\circ }$ clockwise rotation and reflect it in the x - image and find their coordinate.

Explanation of Solution

Given : from the figureprovided in the question, it is observed ,

There is an polygon ABCD in quadrant II, which coordinates are

  $A\left(-4,4\right),B\left(-2,4\right),C\left(-1,1\right),D\left(-3,1\right)$

Graph:

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

  $\begin{array}{l}\left(x,y\right)\to \left(y,-x\right)\\ A\left(-4,4\right)\to A\text{'}\left(4,4\right)\\ B\left(-2,4\right)\to B\text{'}\left(4,2\right)\\ C\left(-1,1\right)\to C\text{'}\left(1,1\right)\\ D\left(-3,1\right)\to D\text{'}\left(3,1\right)\end{array}$

After that for reflect it in the x -axis the final image y -axis coordinates will multiply by -1.

  $\begin{array}{l}\left(x,y\right)\to \left(x,-y\right)\\ A\text{'}\left(4,4\right)\to A\text{'}\text{'}\left(4,-4\right)\\ B\text{'}\left(4,2\right)\to B\text{'}\text{'}\left(4,-2\right)\\ C\text{'}\left(1,1\right)\to C\text{'}\text{'}\left(1,-1\right)\\ D\text{'}\left(1,3\right)\to D\text{'}\text{'}\left(1,-3\right)\end{array}$