To find the coordinates of the vertices after a dilation centered at the origin with a scale factor of 5, you multiply each coordinate of the vertices by the scale factor.
Given the points:
- A = (-1, -2)
- B = (-1, 0)
- C = (2, 0)
- D = (2, -1)
Now, applying the scale factor of 5:
-
For point A: \[ A' = (5 \cdot -1, 5 \cdot -2) = (-5, -10) \]
-
For point B: \[ B' = (5 \cdot -1, 5 \cdot 0) = (-5, 0) \]
-
For point C: \[ C' = (5 \cdot 2, 5 \cdot 0) = (10, 0) \]
-
For point D: \[ D' = (5 \cdot 2, 5 \cdot -1) = (10, -5) \]
Thus, the coordinates of the vertices after dilation are:
- \( A' = (-5, -10) \)
- \( B' = (-5, 0) \)
- \( C' = (10, 0) \)
- \( D' = (10, -5) \)