To graph the image of triangle BCD after a dilation centered at the origin with a scale factor of k = -1/5, we can follow these steps:
1. Plot the vertices B(-5,-10), C(-10,15), and D(0,5) on a coordinate plane.
2. To perform the dilation, we need to multiply the coordinates of each vertex by the scale factor k.
- For vertex B:
- New x-coordinate: -5 * (-1/5) = 1
- New y-coordinate: -10 * (-1/5) = 2
So the new coordinates for B' are (1, 2).
- For vertex C:
- New x-coordinate: -10 * (-1/5) = 2
- New y-coordinate: 15 * (-1/5) = -3
So the new coordinates for C' are (2, -3).
- For vertex D:
- New x-coordinate: 0 * (-1/5) = 0
- New y-coordinate: 5 * (-1/5) = -1
So the new coordinates for D' are (0, -1).
3. Plot the new vertices B'(1,2), C'(2,-3), and D'(0,-1) on the coordinate plane.
4. Connect the new vertices B', C', and D' to form the image triangle B'C'D'.
The resulting image triangle B'C'D' is a scaled-down version of triangle BCD with a scale factor of -1/5.
