∆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 reflection of A', B', and C' across the line y = -x.
The reflection of a point (x, y) across the line y = -x is (-y, -x).
Applying this reflection to A'(-1, 1), we get A(1, -1).
Applying this reflection to B'(-2, -1), we get B(1, 2).
Applying this reflection to C'(-1, 0), we get C(0, 1).
Therefore, the vertices of ∆ABC are A(1, -1), B(1, 2), and C(0, 1).
So, the correct answer is B. A(-1, 1), B(1, 2), C(0, 1).
To find the vertices of ΔABC, we need to find the image of ΔA'B'C' after reflecting it about the line y = -x.
The line y = -x is the line with a slope of -1 passing through the origin (0, 0).
To reflect a point (x, y) about the line y = -x, we swap the x- and y-coordinates and change their signs.
So, for point A'(-1, 1), the reflection will be A(1, -1).
For point B'(-2, -1), the reflection will be B(1, 2).
For point C'(-1, 0), the reflection will be C(0, 1).
Therefore, the vertices of ΔABC are A(1, -1), B(1, 2), and C(0, 1).
Hence, the answer is option B:
A(-1, 1), B(1, 2), C(0, 1)
To find the vertices of ΔABC, we need to find the reflection of each vertex of ΔA'B'C' about the line y = -x.
Let's start with vertex A. The given coordinates of A' are (-1, 1). To find the reflection of A' about y = -x, we swap the x and y-coordinates. Therefore, the x-coordinate of A is 1, and the y-coordinate is -1. So the coordinates of vertex A are (1, -1).
Now, let's move on to vertex B'. The given coordinates of B' are (-2, -1). Again, we swap the x and y-coordinates to find the reflection of B' about y = -x. This gives us a new x-coordinate of -1 and a new y-coordinate of -2. So the coordinates of vertex B are (-1, -2).
Finally, let's find the coordinates of vertex C'. The given coordinates of C are (-1, 0). Swapping the x and y-coordinates, we get a new x-coordinate of 0 and a new y-coordinate of -1. So the coordinates of vertex C are (0, -1).
Putting it all together, the vertices of ΔABC are A(1, -1), B(-1, -2), and C(0, -1).
Therefore, the correct answer is option A. A(1, -1), B(-1, -2), C(0, -1).