Consider a finite set of points, Φ, in the R2, such that they follow the following properties :[*] Φ doesn't contain the origin {(0,0)} and not all points are collinear.
[*] If α∈Φ, then −α∈Φ, cα∈/Φ for c=1 or −1
[*] If α, β are in Φ, then the reflection of β in the line passing through the origin and perpendicular to the line containing origin and α is in Φ
[*] If α=(a,b), β=(c,d), (both α, β∈Φ) then c2+d22(ac+bd)∈ZProve that there cannot be 5 collinear points in Φ number theorySetscoordinate geometry