Math Is Fun Forum

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Co-ordinate Geometry

the angle bisector of two lines ax + by + c = 0 & px + qy + r = 0
is the locus of pts whose perpendicular distance from both lines is same.
We write this mathaematically as

|(aX + bY + c)/sqrrt(a^2 + b^2)| = + or - |(pX + qY + r)/sqrrt(p^2 + q^2)|

How do we differentiate between the two???
ie which one is acute angle bisector and which one is obtuse????

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Co-ordinate Geometry

hi 123ronnie321

The gradient of the first line is given by tan F = -a/b

and for the second, tan S = -p/q

The compound angle formula for tan ( F - S ) then gives

If this is positive then the angle F-S is acute, otherwise obtuse.

Once you have found one bisector, its gradient should reveal where it falls in relation to the two lines.

Unless you want to create a program to do this automatically, I think it is easier in practice simply to inspect the lines on a sketch. (and this will help confirm your answers don't contain computational errors)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Co-ordinate Geometry

thanks bob

yes, graphical method is the best.

sameer mishra

Member

Registered: 2010-08-27

Posts: 64

Re: Co-ordinate Geometry

hello bob you are absolutely wrong

to diffrentiate acute obtuse angle bisector take one line and one bisector

"LET tan(x) is angle between one line and one bisector if [tan(x)<=1]then bisector is acute angle opther wise obtuse angle bisector"

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Co-ordinate Geometry

Hi Sameer,

you are absolutely wrong

That's a bit harsh.

Your method is shorter but does that make mine wrong?

Andrew Wiles took 7 years to prove Fermat's Last Theorem.  Fermat, himself,  claimed a shorter proof.  Does that make Wiles wrong?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Co-ordinate Geometry

Hi Bob

hello bob you are absolutely wrong

Yes, that is harsh. I only hope that it is due to his lack of understanding of our language and customs as you once pointed out.

Hi sameer mishra;

Certainly, attempting to correct someone else's work is difficult. It must be done without hurting the other person's feelings. Without being combative. Other people have the same feelings you do, Bob is not made out of cardboard.

I usually phrase it like this," Hi whomever; I am not getting the same answer as you, could you explain to me what you did? Remember your supposed correction to someone else's stuff could be wrong. He might be right!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Co-ordinate Geometry

Ok,

bob and sameer,

to be honest i am not fully satisfied with either of your answers although they are correct. I think i should be more clear with what i am asking.

Can you say which one is obtuse angle bisector and which one acute just by putting some conditions on a,b,c,p,q,r. Like a computer programme.

If numerical values are given i am able to solve. This is what once our teacher had asked us.