To find the coordinates of the vertices after a dilation with a scale factor of \(\frac{1}{5}\) centered at the origin, you can multiply each of the original coordinates by the scale factor.
Given:
- \(P = (5, -10)\)
- \(Q = (10, -10)\)
- \(R = (10, -5)\)
- \(S = (5, -5)\)
Applying the scale factor \(\frac{1}{5}\):
-
For point \(P'\): \[ P' = \left(5 \cdot \frac{1}{5}, -10 \cdot \frac{1}{5}\right) = (1, -2) \]
-
For point \(Q'\): \[ Q' = \left(10 \cdot \frac{1}{5}, -10 \cdot \frac{1}{5}\right) = (2, -2) \]
-
For point \(R'\): \[ R' = \left(10 \cdot \frac{1}{5}, -5 \cdot \frac{1}{5}\right) = (2, -1) \]
-
For point \(S'\): \[ S' = \left(5 \cdot \frac{1}{5}, -5 \cdot \frac{1}{5}\right) = (1, -1) \]
So, the coordinates of the vertices after the dilation are:
- \(P' = (1, -2)\)
- \(Q' = (2, -2)\)
- \(R' = (2, -1)\)
- \(S' = (1, -1)\)