Determine whether the points are collinear.
`R(0,3),D(2,1) and S(3, -1)`

Explanation

`R(0,3),D(2,1)` and `S(3,-1)`
By distance formula
`d(R,D)=sqrt((2-0)^(2)+(1-3)^(2))`
`=sqrt((2)^(2)+(-2)^(2))`
`=sqrt(4+4)`
`=sqrt(8)`
`=sqrt(2xx2xx2)`
`=2sqrt(2)`……..1
`d(D,S)=sqrt((3-2)^(2)+(-1-1)^(2))`
`=sqrt(1^(2)+(-2)^(2))`
`=sqrt(1+4)`
`=sqrt(5)`......2
`d(R,S)=sqrt((3-0)^(2)+(-1-3)^(2))`
`=sqrt(3^(2)+(-4)^(2))`
`=sqrt(9+16)`
`=sqrt(25)`
`=5`................... 3
Adding 2 and 3
`d(D,S)+d(R,S)=sqrt(5)+5`....4
`:.d(D,S)+(R,S)=sqrt(5)+5`
`:.d(D,S)+d(R,S)!=d(R,D)`
..[From 1 and 1]
`:.` Points R,D and S are not collinear.
Points `R(0,3),D(2,1)` and `S(3,-1)` are not collinear.