Register to reply

Coordinate geometry - bisector of two lines

by jd12345
Tags: bisector, coordinate, geometry, lines
Share this thread:
Feb9-12, 02:55 AM
P: 260
Two lines - a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are given
I know that the equation of its bisectors is
a1x + b1y + c1 / √a1^2 + b1^2 = +- a2x + b2y + c2 / √a2^2 + b2^2

But i intend to find which one is the obtuse angle bisector and which one is the acute angle bisector. I want to find a general formula
Assuming c1 , c2 both are of same sign
My text says if a1a2 + b1b2 > 0 and if we take the positve sign we get the obtuse angle bisector - and after many examples i think its true

But i want to prove it using general equation of line
I tried to find the angle between bisector adn original line
i.e. tan θ = m1 - m2 / 1+ m1m2 and then if it is greater than one it will be of obtuse angle but calculations are tough if we use general equation of line

Any simple proof of the following statement:
Assuming c1 , c2 both are of same sign
IF a1a2 + b1b2 > 0 then if we take positve sing we get the obtuse angle bisector

Thank you!
Phys.Org News Partner Mathematics news on
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture

Register to reply

Related Discussions
Geometry terminology: altitude from vertex, median from vertex, the bisector of angle Precalculus Mathematics Homework 3
Euclidian geometry: Construct circle trough point on angle bisector where... Precalculus Mathematics Homework 1
Geometry Coordinate Precalculus Mathematics Homework 1
What is coordinate system and how to find angles b/w lines General Math 2
Circle geometry- bisector rules vs. perpendicular rules General Math 1