Chapter 12.6, Problem 13E

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.

  $J\left(2,-1\right),K\left(4,-1\right),L\left(4,-5\right),M\left(3,-6\right),N\left(2,-5\right);{180}^{\circ }\text{ rotation}$

Explanation of Solution

Given : the vertices and rotationprovided in the question,

  $J\left(2,-1\right),K\left(4,-1\right),L\left(4,-5\right),M\left(3,-6\right),N\left(2,-5\right);{180}^{\circ }\text{ rotation}$

Graph:

Interpretation : Observed from the graph,

in ${180}^{\circ }$ rotation, there is no switching of coordinates. In this rotation multiply the image both coordinate by -1.

Original   image

  $\begin{array}{l}\left(x,y\right)\to \left(-x,-y\right)\\ J\left(2,-1\right)\to A\left(-2,1\right)\\ K\left(4,-1\right)\to B\left(-4,1\right)\\ L\left(4,-5\right)\to C\left(-4,5\right)\\ M\left(3,-6\right)\to D\left(-3,6\right)\\ N\left(2,-5\right)\to E\left(-2,5\right)\end{array}$

So the image lies in the second coordinate.