Draw the image triangle A2, B2, and C2 of triangle ABC under an anticlockwise rotation through 90° about the origin where A=A2, B=B2, and C= C2

An anticlockwise rotation of $90^\circ$ about the origin transforms a point $(x,y)$ to $(-y,x)$.

• For $A(3,5)$:

• For $B(0,2)$:

• For $C(5,1)$:

So, the vertices of the image triangle are $A_2(-5,3)$, $B_2(-2,0)$, and $C_2(-1,5)$.

• Plot $A_2(-5,3)$: Move 5 units left from the origin, then 3 units up. Label it $A_2(-5,3)$.
• Plot $B_2(-2,0)$: Move 2 units left from the origin, then stay on the x-axis. Label it $B_2(-2,0)$.
• Plot $C_2(-1,5)$: Move 1 unit left from the origin, then 5 units up. Label it $C_2(-1,5)$.

Connect the points $A_2$, $B_2$, and $C_2$ with straight lines to form the rotated triangle.