Final answer:
The coordinates of A'B'C' after dilation by a scale factor of 2 from the origin would be twice the original coordinates. Therefore, option (d) with coordinates (4, 4), (8, 8), and (-8, 4) is the correct answer.
Step-by-step explanation:
To find the coordinates of the vertices of triangle A'B'C' after a dilation by a scale factor of 2 with the center of dilation at the origin, we simply need to multiply the coordinates of the original vertices of triangle ABC by 2. Given that the scale factor is 2, each coordinate (x, y) of the original triangle will become (2x, 2y) in the dilated triangle.
Without the original coordinates of triangle ABC, we cannot determine the exact coordinates of A'B'C', but we can verify which of the given options (a, b, c, d) is consistent with a dilation by a scale factor of 2. We are looking for a set of coordinates where each pair has been multiplied by 2 from their original coordinates.
- Option (a): (1, 2), (2, 2), (-2, 1)
- Option (b): (4, 2), (8, 6), (-8, 2)
- Option (c): (4, 4), (6, 6), (-2, 4)
- Option (d): (4, 4), (8, 8), (-8, 4)
As an example, if the original coordinates of a point were (2, 2), after dilation by a factor of 2, the new coordinates would be (4, 4). Therefore, option (d) is the correct answer because each of the given vertices seems to have coordinates that are twice the original coordinates, which implies a dilation by a scale factor of 2 from the origin.