Question

1. parallelogram mnop with vertices m(1, 7), n(8, 5), o(4, 2), and p(-3, 4): 180°

Explanation:

Step1: Recall rotation rule

A 180 - degree rotation about the origin of a point $(x,y)$ results in the point $(-x,-y)$.

Step2: Apply rule to point M

For point $M(1,7)$, when rotated 180 degrees, $x = 1$ and $y = 7$, so $M'$ is $(-1,-7)$.

Step3: Apply rule to point N

For point $N(8,5)$, when rotated 180 degrees, $x = 8$ and $y = 5$, so $N'$ is $(-8,-5)$.

Step4: Apply rule to point O

For point $O(4,2)$, when rotated 180 degrees, $x = 4$ and $y = 2$, so $O'$ is $(-4,-2)$.

Step5: Apply rule to point P

For point $P(-3,4)$, when rotated 180 degrees, $x=-3$ and $y = 4$, so $P'$ is $(3,-4)$.

Answer:

$M'(-1,-7), N'(-8,-5), O'(-4,-2), P'(3,-4)$