Question

graph the image of rectangle abcd after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Identify original coordinates

Assume $A(-8,6)$, $B(0,6)$, $C(0,8)$, $D(-8,8)$.

Step3: Apply rotation rule to point A

For $A(-8,6)$, using $(x,y)\to(-y,x)$, we get $A'(-6, - 8)$.

Step4: Apply rotation rule to point B

For $B(0,6)$, using $(x,y)\to(-y,x)$, we get $B'(-6,0)$.

Step5: Apply rotation rule to point C

For $C(0,8)$, using $(x,y)\to(-y,x)$, we get $C'(-8,0)$.

Step6: Apply rotation rule to point D

For $D(-8,8)$, using $(x,y)\to(-y,x)$, we get $D'(-8,-6)$.

Step7: Graph new rectangle

Plot points $A'(-6, - 8)$, $B'(-6,0)$, $C'(-8,0)$, $D'(-8,-6)$ and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices $A'(-6, - 8)$, $B'(-6,0)$, $C'(-8,0)$, $D'(-8,-6)$ on the coordinate - plane.