Question

Determine the ratio in which the line 3x + 2y –9 = 0 divides the line segment joining the points(1, 3) and (2, 7).

Answer 1

Let the line 3x + 4y - 9 = 0 divides the line segment joining the points (1,3) and (2,7) in the ratio k:1

then the coordinate of the point is .

Since this the intersection point, it also lies on the line 3x + 4y - 9 = 0.Thus

Since k is negative, the line 3x + 4y - 9 = 0 divides the line segment joining the points (1,3) and (2,7) externally in the ratio 

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