USING DISTANCE FORMULA TO SHOW THAT THE POINTS ARE COLLINEAR

To find the distance between two points (x1, y1) and (x2, y2), we use the formula given below. 

Problem 1 :

Using distance formula, show that the points A (3, 1), B (6, 4) and C (8, 6) are collinear.

Solution :

Distance between points A and B :

Distance between points B and C :

Distance between points C and A :

AB = 3√2, BC = 2√2 and CA = 5√2

AB + BC = CA

3√2 + 2√2 = 5√2

Problem 2 :

Using distance formula show that distance points are collinear (1, −1),(5, 2),(9, 5).

Solution :

Let the given points be A(1, −1) B (5, 2) and C(9, 5).

AB + BC = AC 

5 + 5 = 10

10 = 10

So, the points A, B and C are collinear.