Determine whether the points are collinear.
`L(-2,3), M(1,-3), N(5,4)`

Explanation

`L(-2,3),M(1,-3)` and `N(5,4)`.
By distance formula,
`d(L,M)=sqrt([1-(-2)]^(2)+(-3-3)^(2))`
`=sqrt(3^(2)+(-6)^(2))`
`=sqrt(9+36)`
`=sqrt(45)`
`=sqrt(3xx3xx5)`
`=3sqrt(5)`……1
`d(M,N)=sqrt((5-1)^(2)+[4-(-3)]^(2))`
`=sqrt(4^(2)+7^(2))`
`=sqrt(16+49)`
`sqrt(65)`.........2
`d(L,N)=sqrt([5-(-2)]^(2)+(4-3)^(2))`
`=sqrt(7^(2)+1^(2))`
`=sqrt(49+1)`
`=sqrt(50)`
`=sqrt(5xx5xx2)`
`=5sqrt(2)`...3
Adding 1 and 3
`d(L,M)+d(L,N)=3sqrt(5)+5sqrt(2)`....4
`:.d(L,M)+d(L,N)~=d(M,N)`
..........[From 2 and 4]
`:.` points L,M and N are not collinear.
Points `L(-2,3),M(1,-3)` and `N(5,4)` are not collinear.