Question

question 13
rotate the triangle r(3, 1), s(1, 3), t(4, 5) 180 degrees about the origin.
○ r(-3, -1), s(-1, -3), t(-4, -5)
○ r(3, 1), s(1, -3), t(4, -5)
○ none of the other answers are correct
○ r(1, 3), s(3, 1), t(5, 4)
○ r(-1, -3), s(-3, -1), t(-5, -4)

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point R

For point $R(3,1)$, after 180 - degree rotation about the origin, $x = 3$ and $y = 1$, so the new point $R'$ is $(-3,-1)$.

Step3: Apply rule to point S

For point $S(1,3)$, with $x = 1$ and $y = 3$, the new point $S'$ is $(-1,-3)$.

Step4: Apply rule to point T

For point $T(4,5)$, where $x = 4$ and $y = 5$, the new point $T'$ is $(-4,-5)$.

Answer:

A. $R'(-3,-1),S'(-1,-3),T'(-4,-5)$