Answer:
C = (4, -6)
Step-by-step explanation:
The ratio tells you ...
(B-A)/(C-A) = 2/5
Solving for C, we get ...
5(B-A) = 2(C-A) . . . . cross-multiply
5B -5A = 2C -2A . . . eliminate parenthses
5B -3A = 2C . . . . . . add 2A
C = (5B -3A)/2 . . . . divide by 2
Putting in the coordinate values, we find ...
C = ((5(-2)-3(-6))/2, (5(3)-3(9))/2) = (8/2, -12/2)
C = (4, -6)
