Question

Prove that the following points (in a graph) are collinear:-
(2,-2), (-3,8), (-1,4)

Answer 1

Let mark the points as:
A(2,-2), B(-3,8), B(-1,4)
The distance between the points are as follows
AB=(-3-2)+(8+2)=5
BC=(-1+3)+(4-8)=2
AC=(-1-2)+(4+2)=3
If the point should be collinear the sum of difference of two point is equal to the third one,
therefore,BC+AC=AB,2+3=5
therefore points are collinear

Answer 2

if three points are collinear then they lie in a line
equation of line passing through (2,-2)&(-3,8)
y+2 = -2(x-2)
2x + y = 2
if third point lie on this line then point must satisfy this line
-2+4 = 2
2 = 2
hence points are collinear