Question

By distance formula show that the points (1 , -1); (5 , 2) and (9, 5) are collinear.

Answer 1

Given ,

The three points are A(1 , -1) B(5 , 2) and C(9, 5)

We know that , if three points A , B and C are collinear , then AB + BC = AC

$\boxed{ \sf{Distance = \sqrt{ {( x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} } }}$

Thus ,

AB = √(5 - 1)² + (2 + 1)²

AB = √16 + 9

AB = √25

AB = 5 units

Similarly ,

BC = √(9 - 5)² + (5 - 2)²

BC = √16 + 9

BC = √25

BC = 5 units

Now ,

AC = √(9 - 1)² + (5 + 1)²

AC = √64 + 36

AC = √100

AC = 10 units

It is observed that ,

AB + BC = AC

✭ The given three points are collinear