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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 at (-6,9) and B is at (-2,3), what are the coordinates of point C?

Answer» Here, ratio of `AB` to `AC` is `2:5`.
`:. B` divides `AC` into `2:3` ratio.
Let `(x,y)` are the coordinates of `C`.
Then,
`(2(x)+3(-6))/(2+3) = -2 and (2(y)+3(9))/(2+3) = 3`
`=>(2x+(-18))/5 = -2 and (2y+27)/5 = 3`
`=>2x = -10+18 and y = 2y = 15-27`
`=>x = 4 and y = -6`
So, coordinates of `C` are `(4,-6)`.


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