Grade 12Analytical Geometry
Why do we use +- sign in case of angular bisector and how
1 Answer
Arun
To determine a bisector which lies in the same relative position with respect to the lines as a given point S(x3, y3) does, make the signs of the expressions A1x3 + B1y3+ C1 and A2x3 + B2y3 + C2 identical. (say positive) then (A1x + B1y + C1)/√(A12 + B12) = ± (A2x + B2y + C2)/√(A22 + B22) gives the bisector towards this point. If the signs are different multiply one of the equations with ‘–1’ throughout, so that positive sign is obtained. Then above equation with changed equations of lines will given the required bisector.
If (x3, y3) ≡ (0, 0) and A2A1 + B2B1 > 0 then the bisector towards the origin is the obtuse angle bisector.
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