find the ratio in which the join of the points (1,2) and (-2,3) is divided by the line 3x + 4y = 7

The coordinates of the point which divides the line segment joining the points internally in the ratio are

The given points are .

Thus, the coordinates of the point which divides the line segment joining the points internally in the ratio are  

That is

Since the point lies on the line , it satisfies the equation of theline.

Thus substitute in , we have

Thus, the ratio of the point  which divides the line segment joining the points internally is 4:1

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