Question

a triangle is drawn on a grid with coordinates $a(3, 2)$, $b(0, 2)$, and $c(-1, -2)$.if $\triangle abc$ is rotated $90^{\circ}$ counterclockwise around the origin to produce $\triangle abc$, which statements must be true?select all that apply.$square$ the coordinates of $a$ are $(-2, 3)$.$square$ the coordinates of $b$ are $(2, 0)$.$square$ the coordinates of $b$ are $(1, -2)$ and the coordinates of $c$ are $(-2, 1)$.$square$ the coordinates of $b$ are $(-2, 0)$ and the coordinates of $c$ are $(2, -1)$.

Explanation:

Step1: Recall 90° rotation rule

A point $(x,y)$ rotated 90° counterclockwise around the origin transforms to $(-y,x)$.

Step2: Calculate $A'$ coordinates

For $A(3,2)$: $x=3, y=2$. Apply rule: $(-2, 3)$.

Step3: Calculate $B'$ coordinates

For $B(0,2)$: $x=0, y=2$. Apply rule: $(-2, 0)$.

Step4: Calculate $C'$ coordinates

For $C(-1,-2)$: $x=-1, y=-2$. Apply rule: $(2, -1)$.

Step5: Match with options

Compare calculated coordinates to given statements.

Answer:

The coordinates of $A'$ are $(-2, 3)$.
The coordinates of $B'$ are $(-2, 0)$ and the coordinates of $C'$ are $(2, -1)$.