Chapter 11, Problem 20CR

To determine

To find:Graph each figure and its image after a clockwise rotation about the origin.

Answer to Problem 20CR

Vertices after rotation are

  $\begin{array}{l}G\text{'}\left(-1,0\right)\\ H\text{'}\left(3,-3\right)\\ J\text{'}\left(-3,-2\right)\end{array}$

Explanation of Solution

Given information:

Vertices of $\Delta GHJ$ are

  $\begin{array}{l}G\left(0,-1\right)\\ H\left(3,3\right)\\ J\left(2,-3\right)\end{array}$

  ${270}^0$ clockwise rotation.

When a figure is rotated by ${270}^0$ clockwise the coordinates will be $\left(y,-x\right)$ from the Original.

Using this

Vertices after rotation will be

  $\begin{array}{l}G\left(0,-1\right)\to G\text{'}\left(-1,-0\right)\\ \Rightarrow G\left(0,-1\right)\to G\text{'}\left(-1,0\right)\\ H\left(3,3\right)\to H\text{'}\left(3,-3\right)\\ J\left(2,-3\right)\to J\text{'}\left(-3,-2\right)\end{array}$

Therefore,

Vertices after rotation are

  $\begin{array}{l}G\text{'}\left(-1,0\right)\\ H\text{'}\left(3,-3\right)\\ J\text{'}\left(-3,-2\right)\end{array}$