Question

graph the image of rectangle efgh after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify rectangle vertices

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

Step3: Apply rotation rule to each vertex

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

Answer:

Plot the new rectangle formed by the rotated vertices according to the rule $(x,y)\to(y, - x)$.