Question

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

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