If l is a line and p is a point on l then there exactly one

If l is a line and p is a point on l, then there exactly one line m such that p lies on m and m.l.f

Solution

Given l is a line and there exist a point P on line l.

Now

Contradiction if l and m were same line then there will be more then one points which will be common on both lines.

So, l and m are distincts and nonparallel lines. By definition of nonparallel lines both lines l and m will intersect each other at exact one point.

Let\'s assume there exist a another point Q on both lines l and m, then by theoram there exist exactly one line on which two distinct points lie. Since P and Q both are on line l and m which means l and m are same line, which is not possible.

So there is only one point P, such that it lies on both l and m line.