Determine whether the points are collinear.
`P(-2,3), Q(1,2), R(4,1)`

Explanation

`P(-2,3),Q(1,2)` and `R(4,1)`
By distance formula
`d(P,Q)=sqrt([1-(-2)]^(2)+(2-3)^(2))`
`=sqrt(3^(2)+(-1)^(2))`
`=sqrt(9+1)`
`=sqrt(10)`……..1
`d(Q,R)=sqrt((4-1)^(2)+(1-2)^(2))`
`=sqrt(3^(2)+(-1)^(2))`
`=sqrt(9+1)`
`=sqrt(10)`.......2
`d(P,R)=sqrt([4-(-2)]^(2)+(1-3)^(2))`
`=sqrt(6^(2)+(-2)^(2))`
`=sqrt(36+4)=sqrt(40)`
`=sqrt(2xx2xx2xx5)`
`=2sqrt(10)`............3
Adding 1 and 2 we get
`d(P,Q)+d(Q,R)=sqrt(10)+sqrt(10)`
`:.d(P,Q)+d(Q,R)=2sqrt(10)`......4
`:.d(P,Q)+d(Q,R)=d(P,R)`
......[From 3 and 4]
`:.` points P, Q and R are collinear.
Points `P(-2,3),Q(1,2)` and `R(4,1)` are collinear.