Homework in attachments, it is synthetic geometry. So Ruler Placement Postulate, axioms, and proofs and stuff. those are mostly proofs. i think there is some segment addition stuff as well

Mathematics assignment 4172019
Problem 2:
Let A and B be distinct points in the plane P.
To prove that there exists a coordinate function f: AB to R such that AB={P belongs to AB, :f(P)<=0)
i.e. we have to prove that there is a function f such that
holds good for all points in A and B.
Let us define f(A) = distance of A from origin.
If origin is (0,0) and A has coordinates (x,y) then
, for all points A in the plane P.
Let d(A,B) = distance between A and B
In 2 dimensional plane let f(A) = coordinates = ordered pair = (x,y)
Then we get d(A,B) =- |f(A)-f(B)| for all points A and B
Then we have d(A,B) = negative <0 always
Thus there exists a coordinate function such that f(P)<=0
Problem 1:
To prove for any point P there exists Q such that PQ =1
In two...