Equations of Bisectors of the Angles Between the Lines
Equations of the bisectors of the lines L_{1}: a_{1}x + b_{1}y + c_{1} = 0 and L_{2}: a_{2}x + b_{2}y + c_{2} = 0 (a_{1}b_{2} â‰ a_{2}b_{1}), where c_{1} > 0 and c_{2} > 0 are
= Â±
Conditions

Acute angle bisector

Obtuse angle bisector

a_{1}a_{2} + b_{1}b_{2}> 0

â€“

+

a_{1}a_{2} + b_{1}b_{2}< 0

+

â€“

Note: When both c_{1} and c_{2} are of the same sign, the equation of the bisector of the angle whichcontains the point (Î±, Î²) origin is = , if a_{1}Î± + b_{1}Î² + c_{1 }and a_{2}Î± + b_{2}Î² + c_{2} have the same sign.
Image of a point with respect to the line mirror The image of A(x_{1}, y_{1}) with respect to the line mirror ax + by + c = 0 be B(x_{2}, y_{2}), which is given by
Foot of perpendicular from point A(x_{1}, y_{1}) on the line Let the foot of perpendicular from point A(x_{1}, y_{1}) on the line ax + by + c = 0 be C(x_{3}, y_{3}), which is given by