How to prove three points collinear by Section Formula

Let us understand this concept by taking three points A(2, 5), B(4, 6) and C (8, 8).

Now, we have to prove that the points A(2, 5), B(4, 6) and C (8, 8) are Collinear.

Let B divides AC in the ratio *k* : 1

Then the coordinates of B will be

But the coordinates of B are (4, 6)

Comparing we get

⇒8*k* + 2 = 4*k* + 4 are 8*k* + 5 = 6*k* + 6

⇒8*k* – 4*k* = 4 – 2 are 8*k* – 6*k* = 6 – 5

⇒ 4*k* = 2 are 2*k* = 1

Since the value of *k* is same in both *x* and *y* coordinates

∴ Points A, B and C are collinear.

Hope you get it!!

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