Question

graph the image of rectangle efgh after a rotation 270° counter - clockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - counter - clockwise rotation around the origin is $(x,y)\to(y, - x)$.

Step2: Assume 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 to each vertex

For vertex $E(x_1,y_1)$, the new vertex $E'(y_1,-x_1)$; for $F(x_2,y_2)$, the new vertex $F'(y_2,-x_2)$; for $G(x_3,y_3)$, the new vertex $G'(y_3,-x_3)$; for $H(x_4,y_4)$, the new vertex $H'(y_4,-x_4)$.

Step4: Plot new vertices

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

Since we don't have the actual coordinates of the rectangle's vertices in the question, the general process to graph the rotated rectangle is as above. If we had the coordinates (for example, if $E=(1, - 8)$, $F=(3,-8)$, $G=(3,-6)$, $H=(1,-6)$), for $E=(1, - 8)$: applying the rule $(x,y)\to(y, - x)$ gives $E'=(-8,-1)$; for $F=(3,-8)$ gives $F'=(-8,-3)$; for $G=(3,-6)$ gives $G'=(-6,-3)$; for $H=(1,-6)$ gives $H'=(-6,-1)$. Then we would plot these new points and connect them to form the rotated rectangle.

Answer:

Follow the steps above to graph the rotated rectangle once the coordinates of rectangle $EFGH$ are known. Plot the new vertices obtained by applying the $(x,y)\to(y, - x)$ rotation rule and connect them to form the image of rectangle $EFGH$ after a 270 - degree counter - clockwise rotation around the origin.