Question

triangle def has coordinates d(4, -1), e(5, 2), and f(1, 2). determine the coordinates of the vertices of the image after a rotation 180° about the origin. a) d(5, -1), e(6, 2), and f(2, 2) b) d(1, 0), e(2, 3), and f(-2, 3) c) d(-4, 1), e(-5, -2), and f(-1, -2) d) d(-1, -4), e(2, -5), and f(2, -1)

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point D

Given $D(4, - 1)$, after 180 - degree rotation, $D'=(-4,1)$.

Step3: Apply rule to point E

Given $E(5,2)$, after 180 - degree rotation, $E'=(-5,-2)$.

Step4: Apply rule to point F

Given $F(1,2)$, after 180 - degree rotation, $F'=(-1,-2)$.

Answer:

C. $D'(-4,1),E'(-5,-2),F'(-1,-2)$