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.
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.
I assume you made a sketch . . .
We need some geometry and a half-angle identity.
Find the equation of the bisector of angle of
The coordinates of the vertices are: .Let = bisector ofCode:| C A |(2,3)* * * * (4,3) | * o * | * o * | * * o D | * * o |* * o - - * - - - - - - - - - - - - - - X B
Hence, the bisector of is parallel to the bisector of
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?