Point A is at (6,1) and point C is at (2,-7) find the coordinates of point B on AC such that AB = 1/3BC

  B = (5, -1)

Step-by-step explanation:

We can use the required relation to find an expression for B in terms of the given points.

  AB = (1/3)(BC)

  B -A = (1/3)(C -B)

  B = (1/3)C -(1/3)B +A . . . . . add A

  (4/3)B = (1/3)C +A . . . . . . . add 1/3B

  B = (1/4)C +(3/4)A = (C +3A)/4 . . . . . . multiply by 3/4

  B = ((2, -7) +3(6, 1))/4 = (20/4, -4/4) . . . . . substitute given values

  B = (5, -1)

step-by-step explanation: