Question

graph the polygon with the vertices d(-3, -1), e(-1,2), f(4, -2) and its image after a rotation of 180° about the origin.

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

For point $D(-3,-1)$, after rotation, $x=-3,y = - 1$, so the new point $D'$ is $(3,1)$.

Step3: Apply rule to point E

For point $E(-1,2)$, after rotation, $x=-1,y = 2$, so the new point $E'$ is $(1,-2)$.

Step4: Apply rule to point F

For point $F(4,-2)$, after rotation, $x = 4,y=-2$, so the new point $F'$ is $(-4,2)$.

Step5: Graph the polygons

Graph the original polygon with vertices $D(-3,-1),E(-1,2),F(4,-2)$ and the rotated polygon with vertices $D'(3,1),E'(1,-2),F'(-4,2)$.

Answer:

The vertices of the rotated polygon are $D'(3,1),E'(1,-2),F'(-4,2)$.