Proving there is a unique line m so that l ∩ m = P In my geometry class I'm suppose to prove the following theorem. 
Given line l and point P ∈ l, there is a unique line m so that
l ∩ m = P and the angles formed at the intersection are all right.
I was given the hint that I will need to prove two statements:
first that the line m exists, and secondly that m is unique. However, I'm confused how I would show that line m exists. 
This is what I'm thinking....
Let A and B be distinct points, but are not on line L. Then by definition A and B create line m which is unique. 
I don't really understand how I'n suppose to prove this, could someone please explain or show how I'm suppose to do this proof. 

Since you have $P \in m$, you have a point lying on the required line $m$
and since the angle between $m$ and $l$ is right angle you have the slope of the line $m$, 
and since there is a unique line with a given slope and a point lying on it you can claim that the line $m$ is unique. 
