Chapter 11.5, Problem 24STP

To determine

To graph the figure after clockwise rotation of ${270}^0$ about the origin.

Explanation of Solution

Given:

Figure $ABCD$

  

Calculation for graph of the image:

In figure ABCD the coordinates of vertices are:

  $A(-1,-3),B(-4,-3),C(-4,0),D(-1,0)$

Let A’B’C’D’ be the figure after a clockwise rotation of 270° about the origin.

Now for finding the coordinates of vertices of $A\text{'}B\text{'}C\text{'}D\text{'}$ interchange the x and y coordinates and add a negative sign to the y coordinate.

  $\Rightarrow (x,y)\to (-y,x)$

Coordinates of vertices of $ABCD$	Coordinates of vertices of $A\text{'}B\text{'}C\text{'}D\text{'}$
$A(-1,-3)$	$A\text{'}(3,-1)$
$B(-4,-3)$	$B\text{'}(3,-4)$
$C(-4,0)$	$C\text{'}(0,-4)$
$D(-1,0)$	$D\text{'}(0,-1)$

Now plot $A\text{'}B\text{'}C\text{'}D\text{'}$ on a graph.

Graph:

  

Interpretation:

Figure $ABCD$ was in III quadrant whereas figure $A\text{'}B\text{'}C\text{'}D\text{'}$ in formed in quadrant IV.