Question

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

Explanation:

Step1: Recall rotation rule

A 270 - degree clockwise rotation around the origin has the rule $(x,y)\to(y, - x)$.

Step2: Find coordinates of vertices of original rectangle

Let's assume the coordinates of the vertices of rectangle $EFGH$ are $E(x_E,y_E)$, $F(x_F,y_F)$, $G(x_G,y_G)$, $H(x_H,y_H)$. From the graph, if $E(2,2)$, $F(8,2)$, $G(8,8)$, $H(2,8)$.

Step3: Apply rotation rule to each vertex

For $E(2,2)$: After rotation, $E'(2,-2)$.
For $F(8,2)$: After rotation, $F'(2,-8)$.
For $G(8,8)$: After rotation, $G'(8,-8)$.
For $H(2,8)$: After rotation, $H'(8,-2)$.

Step4: Graph the new rectangle

Plot the points $E'(2,-2)$, $F'(2,-8)$, $G'(8,-8)$, $H'(8,-2)$ on the coordinate - plane and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices $(2,-2)$, $(2,-8)$, $(8,-8)$, $(8,-2)$ on the given coordinate - plane.