∆ABC is reflected about the line y = -x to give ∆A'B'C' with vertices
A'(-1, 1), B'(-2, -1), C(-1, 0). What are the vertices of ∆ABC?
To find the vertices of ∆ABC given the vertices of ∆A'B'C', we can simply reflect ∆A'B'C' back over the line y = -x.
To reflect a point (x, y) over the line y = -x, we swap the x-coordinate and the y-coordinate and change their signs.
1. Reflecting A'(-1, 1):
- Swap the x-coordinate and the y-coordinate: (-1, 1) --> (1, -1)
- Change the signs of both coordinates: (1, -1) --> (-1, 1)
Thus, A = (-1, 1)
2. Reflecting B'(-2, -1):
- Swap the x-coordinate and the y-coordinate: (-2, -1) --> (-1, -2)
- Change the signs of both coordinates: (-1, -2) --> (1, 2)
Thus, B = (1, 2)
3. Reflecting C'(-1, 0):
- Swap the x-coordinate and the y-coordinate: (-1, 0) --> (0, -1)
- Change the signs of both coordinates: (0, -1) --> (0, 1)
Thus, C = (0, 1)
The vertices of ∆ABC are A(-1, 1), B(1, 2), and C(0, 1).