Question

a triangle with vertices at p(1,1), q(3,1), and r(1,5) is translated by the rule (x,y)→(x + 2,y - 3), then rotated 180 - counterclockwise about the origin, and finally reflected across the y - axis. what are the coordinates of the final image of vertex q?
a) q(-5,2)
b) q(5,-2)
c) q(1,4)
d) q(5,2)

Explanation:

Step1: Apply translation rule

For point Q(3,1), using the rule (x,y)→(x + 2,y - 3), we get Q'(3+2,1 - 3)=Q'(5,-2).

Step2: Apply 180 - degree counter - clockwise rotation

The rule for a 180 - degree counter - clockwise rotation about the origin is (x,y)→(-x,-y). For Q'(5,-2), we have Q''(-5,2).

Step3: Apply reflection across y - axis

The rule for reflecting a point (x,y) across the y - axis is (x,y)→(-x,y). For Q''(-5,2), we get Q'''(5,2).

Answer:

D. Q'''(5,2)