Question

write the coordinates of the vertices after a dilation with a scale factor of \\(\frac{1}{2}\\), centered at the origin.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex. From the graph:

• \( R(-6, 4) \)
• \( U(-2, 4) \)
• \( T(-2, 10) \)
• \( S(-6, 10) \)

Step2: Apply dilation formula

The dilation formula centered at the origin with scale factor \( k \) is \( (x, y) \to (kx, ky) \). Here, \( k = \frac{1}{2} \).

For \( R(-6, 4) \):
\( x' = -6 \times \frac{1}{2} = -3 \), \( y' = 4 \times \frac{1}{2} = 2 \), so \( R'(-3, 2) \)

For \( U(-2, 4) \):
\( x' = -2 \times \frac{1}{2} = -1 \), \( y' = 4 \times \frac{1}{2} = 2 \), so \( U'(-1, 2) \)

For \( T(-2, 10) \):
\( x' = -2 \times \frac{1}{2} = -1 \), \( y' = 10 \times \frac{1}{2} = 5 \), so \( T'(-1, 5) \)

For \( S(-6, 10) \):
\( x' = -6 \times \frac{1}{2} = -3 \), \( y' = 10 \times \frac{1}{2} = 5 \), so \( S'(-3, 5) \)

Answer:

\( R'(-3, 2) \), \( U'(-1, 2) \), \( T'(-1, 5) \), \( S'(-3, 5) \)