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We have given two lines $7x-y-11=0$ and $x+y-5=0$ We should find the equations of the lines that are dividing the angles between those two lines on half. I dont know how to approach this problem because I'm not very good in analytical geometry.

I tried finding the angle between the lines, the tg of the angle is $-4/3$, but I dont know how to continue from here.

Thanks in advance.

someone123123
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First find the intersection of the two lines .... Find the angle between the two lines in the form $$\tan \theta = m$$... Use the half angle formula to find the tangent of half the angle between them ....The use sum of angles for tangent to get the slope of the bisector ...To find the constant of the line i.e. $c$ in :$$y=mx+c,$$ the equation of the angle bisector use their intersection... $\blacksquare$

user376343
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MATHS MOD
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  • That seems like far too much work and runs into problems if any of the lines are vertical. It’s much easier to work with the unit direction vectors or normals of the lines: their angle bisectors are simply their sum and difference. – amd Mar 03 '19 at 04:35