SOLUTION: point C lies on line AB such that AC= 3/4 AB. If the endpoints of line AB are A(8,12) and B(-4,0) ,find C. i know i have to use substitution but its been a couple mon

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If straight line AB is divided by the point such that AC:CB = m:n then the projections of AB on x and y axes will also be divided in the same ratio.

Let the coordinates of the points be denoted by the name of the point with a suffix x or y. Thus coordinates of C are (,) and so on.

Considering the projection on x axis,


___________ (1)

In a similar way, ____________ (2)

If the point lies outside the line segment AB then m/n will be negative as AC and CB will be in opposite directions.

Here, , , , and m/n = +- 3 (- sign comes because C may be outside the line segment AB as well). Let m = +-3k and n = k (k = arbitrary constant).

Substituting these in (1) we have

Either or
Either or

Substituting into (2) we have
Either or

So the possible set of coordinates of C are (-1, 3) and (-10, -6).