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Equations of Bisectors of the Angles Between the Lines

Equations of the bisectors of the lines L1: a1x + b1y + c1 = 0 and L2: a2x + b2y + c2 = 0 (a1b2a2b1), where c1 > 0 and c2 > 0 are
 
73115.png = ± 73109.png
 
Conditions
Acute angle bisector
Obtuse angle bisector
a1a2 + b1b2> 0
+
a1a2 + b1b2< 0
+
  
Note: When both c1 and c2 are of the same sign, the equation of the bisector of the angle whichcontains the point (αβ) origin is 73752.png73745.png, if a1α + b1β + c1 and a2α + b2β + c2 have the same sign.

 

Image of a point with respect to the line mirror The image of A(x1, y1) with respect to the line mirror ax + by + c = 0 be B(x2, y2), which is given by
 
73068.png
 
Foot of perpendicular from point A(x1, y1) on the line Let the foot of perpendicular from point A(x1, y1) on the line ax + by + c = 0 be C(x3, y3), which is given by
 
73062.png




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