Question

# Angle ABC has points$A ( - 3,4 ) , B ( - 2,1 ) , \text { and } C ( 2,2 )$. Find the coordinates of the image of the angle after a$90 ^ { \circ }$clockwise rotation about the origin, a translation of 2 units up, and a reflection over the y-axis.

Solution

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We have $\Delta ABC$ with vertices $A(-3,4)$, $B(-2,1)$ and $C(2,2)$.

To rotate $\Delta ABC$\ by an angle of $90\text{\textdegree}$ in the clockwise direction about the origin.

$\bullet$ First plot the graph of $\Delta ABC$\ on the coordinate plane.

$\bullet$ Sketch segment $BO$ connecting point $B(-2,1)$ to the origin $O(0,0)$. Sketch another segment $B'O$, so that the angle between point $B$, $O$ and $B'$ measures $90\text{\textdegree}$ and the segment is the same length as $BO$.

$\bullet$ Do the same with vertex $A(-3,4)$ and $C(2,2)$

The vertices of $\Delta ABC$\ after rotation will be $A'(4,3)$, $B'(1,2)$ and $C'(2,-2)$.

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