Through a given point on a line, there is one and only one line perpendicular to the given line.

Question

The hints that it gave was "Do not limit your thinking to just two dimensions". If it just a regular line there will only be one perpendicular line right?

Answer 1

hold a pencil up. A real pencil. I bet you can make perpendiculars in many directions, because the pencil is in a three dimensional space.

Answer 2

I don't get what you mean by holding up a pencil. I hold up one and I don't see anything?

Answer 3

Let line segment m and n be drawn perpendicularly to point b on line l.
Then ,
Angle mbl =90degree
And angle nbl=90degree
So the two line segment parallel
But two parallel line have no common point
This is contradiction
Therefore,only one perpendicular line can be draw