Prove that two lines are perpendicular if its product's slopes are
Without trig., vectors, just using basic analytic geometry tools.
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Prove that two lines are perpendicular if its product's slopes are
Without trig., vectors, just using basic analytic geometry tools.
What aboutQuote:
Originally Posted by Krizalid
Prove that two lines are perpendicular if its product's slopes are
. :D
I can prove it by trigonometry. Are you sure you do not want that?Quote:
Without trig., vectors, just using basic analytic geometry tools.
(Are we allowed to use conformal mapping :D, ... , just joking).
Algebra, Analytic Geometry: Slopes of Perpendicular Lines
It's full of typos and wrong angles, ugly pictures, and it's too long to be elegant yet the idea seems correct. But then again, I know nothing about proving.
Hello, Krizalid!
I have a rather klunky proof . . .
Quote:
Prove that two lines are perpendicular if the product of their slopes is
Without trig, vectors . . . just using basic analytic geometry tools.
The first problem is creating a right angle.
I used that fact that an angle inscribed in a semicircle is a right angle.Code:|
* * * P
* | o(x,y)
* | o o*
* o o*
o | o
* o | o*
B o-----------+------------o A
(-r,0)* | *(r,0)
|
* | *
* | *
* | *
* * *
|
is a point on the semicircle: .
.[1]
The slope ofis: .
.[2]
The slope ofis: .
.[3]
Substitute [1] into [2]: .
Substitute [1] into [3]: .
Therefore: .