Question

graph the image of rectangle stuv after a rotation $270^{\circ}$ counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

Original points: $S(1, -9)$, $T(7, -9)$, $U(7, -7)$, $V(1, -7)$

Step2: Apply 270° CCW rotation rule

Rotation rule: $(x,y) \to (y, -x)$

• $S'( -9, -1)$: $\text{From } (1,-9): y=-9, -x=-1$
• $T'( -9, -7)$: $\text{From } (7,-9): y=-9, -x=-7$
• $U'( -7, -7)$: $\text{From } (7,-7): y=-7, -x=-7$
• $V'( -7, -1)$: $\text{From } (1,-7): y=-7, -x=-1$

Step3: Plot and connect new points

Plot $S'(-9,-1)$, $T'(-9,-7)$, $U'(-7,-7)$, $V'(-7,-1)$; connect in order.

Answer:

The image rectangle has vertices at $S'(-9, -1)$, $T'(-9, -7)$, $U'(-7, -7)$, $V'(-7, -1)$ (when plotted and connected, this forms the rotated rectangle on the coordinate plane).