write the coordinates of the vertices 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: Find coordinates of point A

The coordinates of point A are $(4,1)$. After rotation, $x = 4,y = 1$, and the new coordinates are $(-1,4)$.

Step3: Find coordinates of point B

The coordinates of point B are $(5,6)$. After rotation, $x = 5,y = 6$, and the new coordinates are $(-6,5)$.

Step4: Find coordinates of point C

The coordinates of point C are $(8,9)$. After rotation, $x = 8,y = 9$, and the new coordinates are $(-9,8)$.

Step5: Find coordinates of point D

The coordinates of point D are $(7,4)$. After rotation, $x = 7,y = 4$, and the new coordinates are $(-4,7)$.

Answer:

A$(-1,4)$, B$(-6,5)$, C$(-9,8)$, D$(-4,7)$