1. **Problem Statement:** We have triangle ABC with vertices A(-2, 10), B(4, 8), and C(2, 4). We need to find the coordinates of A', B', and C' after a dilation with scale factor 3 centered at the origin.
2. **Formula for Dilation:** When a point $(x, y)$ is dilated by a scale factor $k$ about the origin, the new coordinates $(x', y')$ are given by:
$$
(x', y') = (kx, ky)
$$
This means we multiply both the x- and y-coordinates by the scale factor.
3. **Apply the dilation to each vertex:**
- For A(-2, 10):
$$
A' = (3 \times -2, 3 \times 10) = (-6, 30)
$$
- For B(4, 8):
$$
B' = (3 \times 4, 3 \times 8) = (12, 24)
$$
- For C(2, 4):
$$
C' = (3 \times 2, 3 \times 4) = (6, 12)
$$
4. **Final coordinates after dilation:**
- $A' = (-6, 30)$
- $B' = (12, 24)$
- $C' = (6, 12)$
These points match the options given and represent the dilated triangle vertices.
Dilation Coordinates
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