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 rectangle vertices

Let's assume the vertices of rectangle $EFGH$ have coordinates $E(x_1,y_1)$, $F(x_2,y_2)$, $G(x_3,y_3)$, $H(x_4,y_4)$.

Step3: Apply rotation rule

For each vertex, find the new coordinates. For example, if $E(x_1,y_1)$, its new coordinates $E'$ will be $(-x_1,-y_1)$. Do this for all vertices $F$, $G$, and $H$.

Step4: Plot new vertices

Plot the new vertices $E'$, $F'$, $G'$, $H'$ on the coordinate - plane and connect them to form the rotated rectangle.

Answer:

Graph the new rectangle formed by the rotated vertices using the rule $(x,y)\to(-x,-y)$ for each vertex of the original rectangle.