Question

Using distance formula show that these points are COLLINEAR.points are (1,-1), (5,2) , ( 9,5)

Answer 1

Hi friend,

Let these points are A(1,-1) , B(5,2) , C(9,5)

If these points are Collinear then it means,

AB+BC = AC.

Therefore,

using distance formula,

AB² = (5-1)² + (2+1)²

AB² = 16+9 = 25

AB = ✓25 = 5cm

BC² = (9-5)² + (5-2)²

BC² = 16+9 = 25

BC = ✓25 = 5cm

AC² = (9-1)² + (5+1)²

AC² = 64+36

AC² = 100

AC = ✓100 = 10cm

Therefore,

AB + BC = AC

5+5 = 10

10 = 10

HENCE,

THESE POINTS ARE COLLINEAR ....PROVED