Question

graph the image of rectangle jklm 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 vertices

Assume the vertices of rectangle $JKLM$ are $J(x_1,y_1)$, $K(x_2,y_2)$, $L(x_3,y_3)$, $M(x_4,y_4)$. From the graph, if $J(1, - 4)$, $K(9,-4)$, $L(9,-2)$, $M(1,-2)$.

Step3: Apply rotation rule

For point $J(1, - 4)$, after rotation, $J'(-1,4)$.
For point $K(9,-4)$, after rotation, $K'(-9,4)$.
For point $L(9,-2)$, after rotation, $L'(-9,2)$.
For point $M(1,-2)$, after rotation, $M'(-1,2)$.

Step4: Graph new rectangle

Plot the points $J'(-1,4)$, $K'(-9,4)$, $L'(-9,2)$, $M'(-1,2)$ and connect them to form the rotated rectangle.

Answer:

Graph the rectangle with vertices $(-1,4)$, $(-9,4)$, $(-9,2)$, $(-1,2)$.