graph the image of rectangle stuv after a dilation with a scale factor of $\frac{1}{4}$, centered at the…

Explanation:

Step1: Identify original coordinates

Original vertices: $S(-8, 4)$, $T(8, 4)$, $U(8, 8)$, $V(-8, 8)$

Step2: Apply dilation formula

Dilation rule: $(x,y) \to \left(\frac{1}{4}x, \frac{1}{4}y\right)$

• For $S$: $\left(\frac{1}{4} \times -8, \frac{1}{4} \times 4\right) = (-2, 1)$
• For $T$: $\left(\frac{1}{4} \times 8, \frac{1}{4} \times 4\right) = (2, 1)$
• For $U$: $\left(\frac{1}{4} \times 8, \frac{1}{4} \times 8\right) = (2, 2)$
• For $V$: $\left(\frac{1}{4} \times -8, \frac{1}{4} \times 8\right) = (-2, 2)$

Step3: Plot new vertices

Connect $S'(-2,1)$, $T'(2,1)$, $U'(2,2)$, $V'(-2,2)$ to form the dilated rectangle.

Answer:

The vertices of the dilated rectangle are $S'(-2, 1)$, $T'(2, 1)$, $U'(2, 2)$, $V'(-2, 2)$. When plotted and connected, these form the scaled-down rectangle centered at the origin.