A, b and c are collinear, and b is between a and c. the ratio of ab to ac is 2: 5 if a is (-6,9) and b is at (-2,3) what are the coordinates of point c?

  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)

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step-by-step explanation: