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 - counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Identify vertices of rectangle EFGH

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 $E'(y_1,-x_1)$. Similarly for $F$, $G$, and $H$: $F(x_2,y_2)\to F'(y_2,-x_2)$, $G(x_3,y_3)\to G'(y_3,-x_3)$, $H(x_4,y_4)\to H'(y_4,-x_4)$.

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:

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