Chapter 11.5, Problem 23STP

To determine

To find the vertices of $\Delta A\text{'}B\text{'}C\text{'}$ after $\Delta ABC$ is rotated clockwise ${90}^0$ about the origin.

Answer to Problem 23STP

(J) $A\text{'}(2,-1)$ , $B\text{'}(-1,1)$ , $C\text{'}(0,-2)$

Explanation of Solution

Given:

  $\Delta ABC$ with coordinates of vertices as $A(1,2)$ , $B\text{'}(-1,-1)$ and $C(2,0)$

  $\Delta A\text{'}B\text{'}C\text{'}$ is obtained after rotating $\Delta ABC$ by ${90}^0$

Formula used:

When a figure is rotated clockwise by ${90}^0,$ the $x$ and $y$ coordinates interchanges and a negative sign is added to the $x$ coordinate.

  $(x,y)\to (y,-x)$

Calculation:

According to the question, $\Delta A\text{'}B\text{'}C\text{'}$ is obtained after rotating $\Delta ABC$ by ${90}^0$

Now, convert the coordinates of the vertices of $\Delta ABC$ by using $(x,y)\to (y,-x)$ to find the coordinates of $\Delta A\text{'}B\text{'}C\text{'}$ .

So,

Coordinates of vertices of $\Delta ABC$	Coordinates of vertices of $\Delta A\text{'}B\text{'}C\text{'}$
$A(1,2)$	$A\text{'}(2,-1)$
$B\text{'}(-1,-1)$	$B\text{'}(-1,1)$
$C(2,0)$	$C\text{'}(0,-2)$

So, the coordinates of vertices of $\Delta A\text{'}B\text{'}C\text{'}$ are $A\text{'}(2,-1)$ , $B\text{'}(-1,1)$ , $C\text{'}(0,-2).$

Conclusion:

Hence, option (J) $A\text{'}(2,-1)$ , $B\text{'}(-1,1)$ , $C\text{'}(0,-2)$ is correct.