Question

1. 180° rotation

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Assume the coordinates of point $K$ are $(1, - 1)$, $L$ are $(2,-3)$, $M$ are $(1,-5)$ and $N$ are $(3,-3)$.

Step3: Apply rotation rule to $K$

For point $K(1,-1)$, after 180 - degree rotation, $K'$ has coordinates $(-1,1)$.

Step4: Apply rotation rule to $L$

For point $L(2,-3)$, after 180 - degree rotation, $L'$ has coordinates $(-2,3)$.

Step5: Apply rotation rule to $M$

For point $M(1,-5)$, after 180 - degree rotation, $M'$ has coordinates $(-1,5)$.

Step6: Apply rotation rule to $N$

For point $N(3,-3)$, after 180 - degree rotation, $N'$ has coordinates $(-3,3)$.

Answer:

$K'(-1,1)$, $L'(-2,3)$, $M'(-1,5)$, $N'(-3,3)$