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Solved question to find the equation of the angle bisector of the angles between the lines

2x + y = 5 and x - 2y = 1.

Y=-2x+5…(i) y=x/2-1/2…(ii)

Slope of first line

m1=-2 , tan(-2)= -0.03492077 degrees=a

Slope of second line

m2=1/2 , tan(1/2)= 0.00872687 degrees=b

The angle of the bisector is =(b-a)/2

=(0.00872687+0.03492077)/2

=0.0218237degrees

Tan(0.0218237degrees)= 0.0003809

Equation of the bisector will be

Y=0.0003809x+c…(iii)

From (i) & (ii)

-2x+5=x/2-1/2

-5x/2=-11/2

X=11/5

Putting the value of x in (i) we have

Y=-22/5+5=3/5

So the bisector will pass through (11/5,3/5)

(iii) will become

3/5=0.0003809*11/5+c

3/5-0.0041899/5=c

0.599162=c

Required equation of line

Y=0.0003809x+0.599162