(2) (4, 2)
Explanation
Let the coordinates of C be (x, y). Then
BC = 5
x2 + (y + 1)2 = 52 .....(1)
Since AB ^ AC, therefore
2y –6 = –x + 2 x = –2y + 8 ..... (2)
from (1) and (2)(–2y +8)2 + (y +1)2 = 52
5y2 –30y + 40 = 0
y2 –6y + 8 = 0 , y = 2, 4
Putting y = 2 and y = 4 in (2), we get x = 4, x =0 respectively Hence, the coordinates of C are (4, 2) or (0,4)