Triangle ABC has vertices A(–3, 1) , B(–2, 3) and C(–1, 1) . Complete the vertices of the image of △ABC after a rotation of 90° counterclockwise about C.

Answer 1

When you rotate point (x,y) around the origin, you get (-y,x). So, steps to rotate around an arbitrary point X is as follows.

1. Translate so that the image of X is the origin.
2. Rotate around the origin.
3. Translate the origin back to X.

In this case, you first translate ABC so that C aligns with the origin, i.e. moves -(-1) along the X-axis and -1 along the Y-axis. This sends A to (-2,0) and B to (-1,2).

Rotate 90 degrees counterclockwise yields (0,-2) and (-2,-1).

Finally, translate back to C, i.e. moves -1 along the X-axis and 1 along the Y-axis. The final image is A(-1,-1), B(-3,0), C(-1,1).

Answer 2

Answer: If you draw the triangle on x-y graph, you will find that it is an an isosceles triangle. You can easily draw the triangle after the rotation also.

After rotation: A (-1,-1); B (-3,0); C (-1,1)