Question

graph the image of rectangle stuv after a dilation with a scale factor of \\(\frac{1}{4}\\), centered at the origin.

Explanation:

Step1: Identify coordinates of vertices

From graph: \( S(-8,4) \), \( T(8,4) \), \( U(8,8) \), \( V(-8,8) \)

Step2: Apply dilation rule

Dilation center origin: \( (x,y) \to (\frac{1}{4}x, \frac{1}{4}y) \)
\( S' = (-8 \times \frac{1}{4}, 4 \times \frac{1}{4}) = (-2,1) \)
\( T' = (8 \times \frac{1}{4}, 4 \times \frac{1}{4}) = (2,1) \)
\( U' = (8 \times \frac{1}{4}, 8 \times \frac{1}{4}) = (2,2) \)
\( V' = (-8 \times \frac{1}{4}, 8 \times \frac{1}{4}) = (-2,2) \)

Step3: Plot image vertices

Connect \( S'(-2,1) \), \( T'(2,1) \), \( U'(2,2) \), \( V'(-2,2) \)

Answer:

The image rectangle has vertices \( S'(-2,1) \), \( T'(2,1) \), \( U'(2,2) \), \( V'(-2,2) \) (plot these points and connect them).