Question

each figure after the given transformation. 2) rotation 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: Identify original points

Let's assume the coordinates of points $L$, $M$, $K$, $N$ are $L(x_1,y_1)$, $M(x_2,y_2)$, $K(x_3,y_3)$, $N(x_4,y_4)$. From the graph, if $L(1,0)$, $M(- 3,-1)$, $K(0,-4)$, $N(-4,-4)$.

Step3: Apply rotation rule

For point $L(1,0)$: $(1,0)\to(-1,0)$.
For point $M(-3,-1)$: $(-3,-1)\to(3,1)$.
For point $K(0,-4)$: $(0,-4)\to(0,4)$.
For point $N(-4,-4)$: $(-4,-4)\to(4,4)$.

Answer:

The new coordinates of the vertices of the rotated figure are $L'(-1,0)$, $M'(3,1)$, $K'(0,4)$, $N'(4,4)$