Question

1. d(-3, -1), e(-1, 2), f(4, -2); 180°

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 $D(-3,-1)$, when rotated 180 degrees, $x=-3,y = - 1$. Then $(-3,-1)\to(3,1)$.

Step3: Apply rule to point E

For point $E(-1,2)$, when rotated 180 degrees, $x=-1,y = 2$. Then $(-1,2)\to(1,-2)$.

Step4: Apply rule to point F

For point $F(4,-2)$, when rotated 180 degrees, $x = 4,y=-2$. Then $(4,-2)\to(-4,2)$.

Answer:

The new coordinates are $D'(3,1),E'(1,-2),F'(-4,2)$