Question

Angle ABC has points

A(3,4),B(2,1), and C(2,2)A ( - 3,4 ) , B ( - 2,1 ) , \text { and } C ( 2,2 )

. Find the coordinates of the image of the angle after a

9090 ^ { \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 ΔABC\Delta ABC with vertices A(3,4)A(-3,4), B(2,1)B(-2,1) and C(2,2)C(2,2).

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

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

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

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

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

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