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
⇒8k + 2 = 4k + 4 are 8k + 5 = 6k + 6
⇒8k – 4k = 4 – 2 are 8k – 6k = 6 – 5
⇒ 4k = 2 are 2k = 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!!