Question

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), and r(-1, 3) b) p(1, -5), q(-1, -2), and r(3, 1) c) p(-5, -1), q(-2, 1), and r(1, -3) d) p(-5, 1), q(-2, -1), and r(1, -3)

Explanation:

Step1: Recall rotation rule for 180 - degree

When rotating a point $(x,y)$ 180 - degrees about the origin, the new coordinates are $(-x,-y)$.

Step2: Apply rule to point P(-1, 5)

For $P(-1,5)$, new $x=-(-1) = 1$ and new $y=-5$, so new $P(1, - 5)$.

Step3: Apply rule to point Q(1, 2)

For $Q(1,2)$, new $x=-1$ and new $y=-2$, so new $Q(-1,-2)$.

Step4: Apply rule to point R(-3, -1)

For $R(-3,-1)$, new $x=-(-3)=3$ and new $y = -(-1)=1$, so new $R(3,1)$.

Answer:

B) $P(1, - 5), Q(-1,-2), R(3,1)$