Question

graph the image of rectangle efgh 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 coordinates

Assume $E(-7,3)$, $F(-6,3)$, $G(-6,8)$, $H(-7,8)$.

Step3: Apply rotation rule to E

For point $E(-7,3)$, after rotation, $E'=(7, - 3)$.

Step4: Apply rotation rule to F

For point $F(-6,3)$, after rotation, $F'=(6,-3)$.

Step5: Apply rotation rule to G

For point $G(-6,8)$, after rotation, $G'=(6,-8)$.

Step6: Apply rotation rule to H

For point $H(-7,8)$, after rotation, $H'=(7,-8)$.

Step7: Graph new points

Plot points $E'(7, - 3)$, $F'(6,-3)$, $G'(6,-8)$, $H'(7,-8)$ and connect them to form the rotated rectangle.

Answer:

Graph the rectangle with vertices $E'(7, - 3)$, $F'(6,-3)$, $G'(6,-8)$, $H'(7,-8)$ on the given coordinate - plane.