Prove that two lines are perpendicular if its product's slopes are
Without trig., vectors, just using basic analytic geometry tools.
Printable View
Prove that two lines are perpendicular if its product's slopes are
Without trig., vectors, just using basic analytic geometry tools.
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 of is: . .[2]
The slope of is: . .[3]
Substitute [1] into [2]: .
Substitute [1] into [3]: .
Therefore: .