Question

How to prove collinear by section formula?

Answer 1

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The section formula tells us the coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m:n. ... The section formula is helpful in coordinate geometry; for instance, it can be used to find out the centroid, incenter and excenters of a triangle.

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Answer 2

Let C(-1,1) divides AB in the ratio of k : 1

Using section formula, we have:

(k - 3)/(k + 1) = -1 … (1)

(3k - 1)/(k + 1) = 1 … (2)

From (1),

k - 3 = -k - 1

2k = 2

k = 1

Thus, C divides AB in the ratio 1: 1, that is, C is the mid-point of AB.

 A, B and C are collinea