Find the equation of the bisector of angleAof the triangle, the coordinates of whose vertices areA(4,3) , B(0,0) and C(2,3). Please give its solution. Thanks a lot for your help.

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- August 23rd 2009, 07:37 AMninniHelp with equation of the bisector of an angle in a triangle
Find the equation of the bisector of angle

**A**of the triangle, the coordinates of whose vertices are**A(4,3) , B(0,0) and C(2,3)**. Please give its solution. Thanks a lot for your help. - August 23rd 2009, 08:15 AMred_dog
The equation of the side AB:

The equation of the side AC:

Let M(x,y) be a point of the bisector. Then

We get two equations: and

These are the equations of both bisectors, interior and exterior. To find which of them is the interior bisector, plug the coordinates of B and C in the left side member of the equations and we have to get two values of opposite signs. - August 23rd 2009, 08:24 AMPlato
Here is a hint.

If are vectors then the bisector of the angle between them is . - August 23rd 2009, 08:27 AMSoroban
Hello, ninni!

I assume you made a sketch . . .

We need some geometry and a half-angle identity.

Quote:

Find the equation of the bisector of angle of

The coordinates of the vertices are: .

Code:`| C A`

|(2,3)* * * * (4,3)

| * o *

| * o *

| * * o D

| * * o

|* * o

- - * - - - - - - - - - - - - - - X

B

Note that

Hence, the bisector of is parallel to the bisector of

.Let

The slope of is: .

The slope of is: . .

You have the slope of the angle bisector,

. . and a point on the angle bisector

You can now write its equation, right?