Question

using distant formula show that the poi ts (-1,2), (5,0) and (2,1) are collinear​

Answer 1

The points will be colinear if the area formed by these 3 points is 0...

now we know that the area of a triangle with the vertices (x1,y1);(x2,y2)and(x3,y3) is..

$= \frac{1}{2} (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))$

now ...the area formed by these given points is

$= \frac{1}{2} (( - 1)(0 - 1) + 5(1 - 2) + 2(2 - 0)) \\ = \frac{1}{2} (1 - 5 + 4) \\ = \frac{1}{2} \times 0 \\ = 0$

therefore..the given points are colinear.(proved)