Question

graph the image of rectangle klmn after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Assume the coordinates of the vertices of rectangle $KLMN$ are $K(x_1,y_1)$, $L(x_2,y_2)$, $M(x_3,y_3)$, $N(x_4,y_4)$. Let's say from the graph, if $K(-9,5)$, $L(-2,5)$, $M(-2,9)$, $N(-9,9)$.

Step3: Apply rotation rule

For point $K(-9,5)$: $(-9,5)\to(9, - 5)$.
For point $L(-2,5)$: $(-2,5)\to(2,-5)$.
For point $M(-2,9)$: $(-2,9)\to(2,-9)$.
For point $N(-9,9)$: $(-9,9)\to(9,-9)$.

Step4: Graph new points

Plot the points $(9, - 5)$, $(2,-5)$, $(2,-9)$, $(9,-9)$ and connect them to form the rotated rectangle.

Answer:

Graph the rectangle with vertices $(9, - 5)$, $(2,-5)$, $(2,-9)$, $(9,-9)$.