If the point P (m, 3) lies on the line segment joining the points A( and B (2, 8), find the value of m.


It is said that the point P(m,3) lies on the line segment joining the points A( and B (2, 8).

Hence we understand that these three points are collinear. So the area enclosed by them should be 0.

Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)

= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

Given that area of ∆ABP = 0

∴ 0 = |m(6 – 8) - (8 – 3) + 2(3 – 6)|

∴ -2m – 2 -6 = 0

-2m = 8

m = -4

Hence the value of m = -4

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