Chapter 11.5, Problem 22STP

To determine

To find the best option which describes the rotation of $\Delta XYZ$ about the origin to $\Delta X\text{'}Y\text{'}Z\text{'}$ .

Answer to Problem 22STP

(C) ${180}^0$ clockwise about origin.

Explanation of Solution

Given:

  $\Delta XYZ$ and $\Delta X\text{'}Y\text{'}Z\text{'}$

  

Formula used:

When a figure is rotated clockwise by ${180}^0,$ the $x$ and $y$ coordinate changes to $-x$ and $-y$ .

  $(x,y)\to (-x,-y)$

By observing the given graph, the coordinates of vertices of $\Delta XYZ$ and $\Delta X\text{'}Y\text{'}Z\text{'}$ are,

Coordinates of vertices of $\Delta XYZ$	Coordinates of vertices of $\Delta X\text{'}Y\text{'}Z\text{'}$
$X(-4,4)$	$X\text{'}(4,-4)$
$Y(-1,1)$	$Y\text{'}(1,-1)$
$Z(-4,1)$	$Z\text{'}(4,-1)$

From the table it is observed that $(x,y)$ coordinate is changed into $(-x,-y)$ .

So, the $\Delta XYZ$ is rotated by ${180}^0$ in clockwise direction.

Conclusion:

Hence, option (C) is correct.