Point Q of quadrilateral QRST is (-9,2). What is the image of Q after QRST has been reflected acrossthe y-axis and then rotated 90 degrees about the origin?• (2,-2).• (-29)(9,2)None of the other answers are correct• (-9,-2)

Answer:(-2,9)(2,-9)Step-by-step explanation:The point Q of quadrilateral QRST has coordinate (-9,2).When this point is reflected across the y-axis , we negate the x-coordinate to obtain [tex](--9,2)=(9,2)[/tex].This point is again rotated through an angle of 90 degrees(counterclockwise) about the origin.The rule for 90 degrees counterclockwise rotation is [tex](x,y)\to(-y,x)[/tex].[tex]\implies (9,2)\to(-2,9)[/tex]Therefore the image of Q(-9,2) after a reflection across the y-axis followed by a 90 degrees counterclockwise rotation about the origin is is Q'(-2,9).However, the rotation could also be clockwise. The rule for 90 degrees clockwise rotation is [tex](x,y)\to(y,-x)[/tex].[tex]\implies (9,2)\to(2,-9)[/tex]The image of Q(-9,2) after a reflection across the y-axis followed by a 90 degrees clockwise rotation about the origin is is Q'(2,-9).Both answers are there, so you can check them since the question did not specify the direction.