Question

through a given point on a line, there is one and only one line perpendicular to the given line. true or false?

oh and also please please explain why the answer is so. I'm really trying to understand this but i can't :(

Answer 1

true. Let's say these are the perpendicular lines.

Answer 2

They have negative reciprocal slopes. You can draw an infinite amount of lines through that intersection point, but it's not possible to draw a line through that point that's perpendicular to either of the original lines. At least in 2 dimensions

Answer 3

ah ok ok

Answer 4

Of course if you expand this to consider 3 dimensions, the statement is false.
At each corner 3 lines intersect and each is perpendicular to the other 2.