Given a scale factor of one-half , find the coordinates for the dilation of the triangle with vertices at (0, 0), (0, 2), and (4, 0). The center of the dilation is the origin.
1. (0, 0), (0, 4), (8, 0)
2. (0, 0), (0, 1), (2, 0)
3. (one-half,one-half), (one-half, 1), (2, one-half)
4. (2, 2), (2, 4), (8, 2)
To find the dilation of a triangle with a scale factor of one-half, we multiply the x and y coordinates of each vertex by one-half.
Original triangle vertices: (0, 0), (0, 2), (4, 0)
Dilated triangle vertices: (0*1/2, 0*1/2), (0*1/2, 2*1/2), (4*1/2, 0*1/2)
Simplified coordinates: (0, 0), (0, 1), (2, 0)
Therefore, the dilation of the triangle with a scale factor of one-half and the center of dilation at the origin is option 2: (0, 0), (0, 1), (2, 0).