Question

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

Explanation:

Step1: Identify original coordinates

$S(0, 3), T(7, 3), U(7, 10), V(0, 10)$

Step2: Apply rotation rule

For a $270^\circ$ counterclockwise rotation around the origin, the transformation rule is $(x, y) \to (y, -x)$.

• $S'(3, 0)$: $\text{From } (0,3) \to (3, -0)$
• $T'(3, -7)$: $\text{From } (7,3) \to (3, -7)$
• $U'(10, -7)$: $\text{From } (7,10) \to (10, -7)$
• $V'(10, 0)$: $\text{From } (0,10) \to (10, -0)$

Step3: Plot and connect points

Plot $S'(3, 0)$, $T'(3, -7)$, $U'(10, -7)$, $V'(10, 0)$ and connect them to form the rotated square.

Answer:

The coordinates of the rotated square $S'T'U'V'$ are $S'(3, 0)$, $T'(3, -7)$, $U'(10, -7)$, $V'(10, 0)$. When plotted on the grid, these points form the image of the original square after the $270^\circ$ counterclockwise rotation around the origin.