To perform a dilation with a scale factor of \( \frac{1}{4} \) centered at the origin, you multiply each coordinate of the vertices by the scale factor.
Given the vertices:
- \( R = (-8, -8) \)
- \( S = (-8, 8) \)
- \( T = (0, -8) \)
Now, apply the scale factor of \( \frac{1}{4} \) to each vertex:
-
For vertex \( R' \): \[ R' = \left(-8 \cdot \frac{1}{4}, -8 \cdot \frac{1}{4}\right) = \left(-2, -2\right) \]
-
For vertex \( S' \): \[ S' = \left(-8 \cdot \frac{1}{4}, 8 \cdot \frac{1}{4}\right) = \left(-2, 2\right) \]
-
For vertex \( T' \): \[ T' = \left(0 \cdot \frac{1}{4}, -8 \cdot \frac{1}{4}\right) = \left(0, -2\right) \]
Thus, the coordinates of the vertices after the dilation are:
- \( R' = (-2, -2) \)
- \( S' = (-2, 2) \)
- \( T' = (0, -2) \)