Question

1. triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determine the coordinates of the vertices of the image after a reflection in the y - axis. a) p(1, 5), q( - 1, 2), r(3, - 1) b) p( - 1, 5), q(1, 2), r( - 3, - 1) c) p(1, 5), q( - 1, 2), r(3, 1) d) p( - 1, 5), q(1, 2), r( - 3, 1) 14) triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determine the coordinates of the vertices of the image after a rotation 180° about the origin. a) p(5, 1), q(2, 1), r( - 1, 3) b) p(1, - 5), q( - 1, - 2), r(3, 1) c) p( - 5, - 1), q( - 2, - 1), r( - 1, 3) d) p( - 5, - 1), q( - 2, - 1), r(1, - 3)

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Rotate point P

Given $P(-1,5)$, after 180 - degree rotation about the origin, $P'=(1, - 5)$.

Step3: Rotate point Q

Given $Q(1,2)$, after 180 - degree rotation about the origin, $Q'=(-1,-2)$.

Step4: Rotate point R

Given $R(-3,-1)$, after 180 - degree rotation about the origin, $R'=(3,1)$.

Answer:

P'(1, - 5), Q'(-1,-2), R'(3,1)