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Angle Bisector and its properties - Reflection property

Angle Bisector

Angle bisector is locus of point $P(h,k)$ which move such that perpendicular distance of point from lines $L_1=0$ and $L_2=0$ are equal. If the lines $L_1\,:\,a_1x+b_1y+c_1=0$ and $L_2\,:\,a_2x+b_2y+c_2=0$ intersect at point $Q$ i.e $\vert \cfrac{a_1h+b_1k+c_1}{\sqrt{a_1^2+b_1^2}} \vert = \vert \cfrac{a_2h+b_2k+c_2}{\sqrt{a_2^2+b_2^2}} \vert$ Now Replace $(h,k)\rightarrow (x,y)$ we get bisectors $B_1=0\;,\;B_2=0$. $$\Rightarrow \Bigl( \cfrac{a_1x+b_1y+c_1}{\sqrt{a_1^2+b_1^2}}\Bigr)=\pm \Bigl( \cfrac{a_2x+b_2y+c_2}{\sqrt{a_2^2+b_2^2}}\Bigr) $$ Let … Continue reading Angle Bisector