Question

Not understanding about angle bisectors concept in straight lines

Answer 1

Angle bisector of two lines i.e. the line which bisects the angle between the two lines is the locus of a point which is equidistant from the two lines. In other words, an angle bisector has equal perpendicular distance from the two lines.
Let us now try to find the equation of angle bisector. Consider the figure given below:
Suppose we have two lines
L1 : A1x + B1y + C1 = 0
L2 : A2x + B2y + C2 = 0
If point R(p, q) lies on the bisector, then length of perpendicular from the point R to both the lines should be equal.
i.e.
Generalizing for any point (x, y), the equation of the angle bisector is obtained as:
(A1x + B1y + C1)/√(A12 + B12) = + (A2 x+ B2y + C2)/√(A22 + B22)
Note:
This equation gives two bisectors: one-acute angle bisector and the other obtuse bisector.