Question

graph the image of square 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 original coordinates

Assume the coordinates of the vertices of square $JKLM$ are $J(x_1,y_1)$, $K(x_2,y_2)$, $L(x_3,y_3)$, $M(x_4,y_4)$. For example, if $J(- 4,-8)$, $K(-2,-8)$, $L(-2,-6)$, $M(-4,-6)$.

Step3: Apply rotation rule

For point $J(-4,-8)$, after rotation, the new coordinates are $J'(8, - 4)$. For $K(-2,-8)$, the new coordinates are $K'(8,-2)$. For $L(-2,-6)$, the new coordinates are $L'(6,-2)$. For $M(-4,-6)$, the new coordinates are $M'(6,-4)$.

Step4: Plot new points

Plot the points $J'$, $K'$, $L'$, $M'$ on the coordinate plane and connect them to form the rotated square.

Answer:

Graph the new square with vertices obtained by applying the $(x,y)\to(-y,x)$ rule to the original vertices of square $JKLM$.