Chapter 11, Problem 21CR

To determine

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

Answer to Problem 21CR

Vertices after rotation are

  $\begin{array}{l}N\text{'}\left(1,-1\right)\\ P\text{'}\left(3,-2\right)\\ Q\text{'}\left(2,-4\right)\\ R\text{'}\left(-2,-4\right)\end{array}$

Explanation of Solution

Given information:

Vertices of $\Delta GHJ$ are

  $\begin{array}{l}N\left(1,1\right)\\ P\left(2,3\right)\\ Q\left(4,2\right)\\ R\left(4,-2\right)\end{array}$

  ${90}^0$ clockwise rotation.

When a figure is rotated by ${90}^0$ clockwise the coordinates will be $\left(y,-x\right)$ from the Original.

Using this

Vertices after rotation will be

  $\begin{array}{l}N\left(1,1\right)\to N\text{'}\left(1,-1\right)\\ P\left(2,3\right)\to P\text{'}\left(3,-2\right)\\ Q\left(4,2\right)\to Q\text{'}\left(2,-4\right)\\ R\left(4,-2\right)\to R\text{'}\left(-2,-4\right)\end{array}$

Therefore,

Vertices after rotation are

  $\begin{array}{l}N\text{'}\left(1,-1\right)\\ P\text{'}\left(3,-2\right)\\ Q\text{'}\left(2,-4\right)\\ R\text{'}\left(-2,-4\right)\end{array}$

Graph of the given figure after rotation is