ANSWER
A'(1, -1), B'(6, 3), C'(6, -1)
EXPLANATION
We have triangle ABC, and we have to rotate it about vertex A 90 degrees counterclockwise,
Usually, when the center of rotation is the origin, the coordinates of each point exchange and the x-coordinate becomes negative (x, y) → (-y, x). But in this case, the center of rotation is A(1, -1).
If we translate the origin to point A, the new coordinates of the points would be,
Rotating these points about the new origin, the coordinates on the red coordinate plane are,
[tex]\begin{gathered} A^{\prime}(0,0)\rightarrow A^{\prime}^{\prime}(0,0) \\ B^{\prime}(4,-5)\rightarrow B^{\prime}^{\prime}(5,4) \\ C^{\prime}(0,-5)\rightarrow C^{\prime}^{\prime}(5,0) \end{gathered}[/tex]
Let's graph these points,
Now, these points, in the original coordinate plane, have the coordinates,
Hence, the coordinates of the translated vertices are A'(1, -1), B'(6, 3), and C'(6, -1).
