Question

graph the image of rectangle jklm after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Identify vertices of rectangle

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 $J(- 8,-10)$, $K(-4,-10)$, $L(-4,-2)$, $M(-8,-2)$.

Step3: Apply rotation rule to each vertex

For $J(-8,-10)$: $(-8,-10)\to(10, - 8)$.
For $K(-4,-10)$: $(-4,-10)\to(10,-4)$.
For $L(-4,-2)$: $(-4,-2)\to(2,-4)$.
For $M(-8,-2)$: $(-8,-2)\to(2,-8)$.

Step4: Graph the new rectangle

Plot the new vertices $(10, - 8)$, $(10,-4)$, $(2,-4)$, $(2,-8)$ and connect them to form the rotated rectangle.

Answer:

Graph the rectangle with vertices $(10, - 8)$, $(10,-4)$, $(2,-4)$, $(2,-8)$.