∆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?
A.
A(1, -1), B(-1, -2), C(0, -1)
B.
A(-1, 1), B(1, 2), C(0, 1)
C.
A(-1, -1), B(-2, -1), C(-1, 0)
D.
A(1, 1), B(2, -1), C(1, 0)
E.
A(1, 2), B(-1, 1), C(0, 1)
To find the vertices of ∆ABC, we need to find the line of reflection and then reflect the vertices of ∆A'B'C' about that line.
The line of reflection is y = -x, which means that for each point (x, y), it will be reflected to the point (-y, -x).
For ∆A'B'C', the vertices are A'(-1, 1), B'(-2, -1), and C'(-1, 0).
Reflecting A'(-1, 1) about the line y = -x gives us the point (-1, -1), which corresponds to A in ∆ABC.
Reflecting B'(-2, -1) about the line y = -x gives us the point (1, 2), which corresponds to B in ∆ABC.
Reflecting C'(-1, 0) about the line y = -x gives us the point (0, 1), which corresponds to C in ∆ABC.
Therefore, the vertices of ∆ABC are A(-1, -1), B(1, 2), C(0, 1).
The correct answer is C.