Triangle ABC has vertices A(1, 0), B(0, −2) and C(3, −3). If triangle ABC is rotated 90◦ counterclockwise about A, what are the coordinates of the image of C?

Plotting the points on the coordinate plane, we know that C'A forms a 90 degree angle with CA. The slope of CA is -3/2 so the slope of C'A is 2/3. The distance CA is sqrt13 so C'A is also sqrt13. Therefore C' is (-2,-2).

Triangle ABC has vertices A(1, 0), B(0, −2), and C(3, −3). If triangle ABC is rotated 90º counterclockwise about A, what are the coordinates of the image of C?