Question

graph the image of trapezoid stuv after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

Original vertices: $S(-3, -3)$, $T(2, -3)$, $U(2, 3)$, $V(0, 3)$

Step2: Apply dilation rule

Dilation formula: $(x,y) \to (3x, 3y)$

• $S' = (3\times-3, 3\times-3) = (-9, -9)$
• $T' = (3\times2, 3\times-3) = (6, -9)$
• $U' = (3\times2, 3\times3) = (6, 9)$
• $V' = (3\times0, 3\times3) = (0, 9)$

Step3: Plot new vertices

Plot $S'(-9,-9)$, $T'(6,-9)$, $U'(6,9)$, $V'(0,9)$ and connect to form the dilated trapezoid.

Answer:

The vertices of the dilated trapezoid $S'T'U'V'$ are $S'(-9, -9)$, $T'(6, -9)$, $U'(6, 9)$, $V'(0, 9)$. When plotted on the grid, these points form the scaled image of the original trapezoid.