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Find an equation of the angle bisector of the obtuse angles formed by the lines 2x+6y= 9 and x-3y= -2. sketch the given lines and angle bisector.

Find an equation of the angle bisector of the obtuse angles formed by the lines 2x+6y= 9 and x-3y= -2. sketch the given lines and angle bisector.

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hi student,

2x+6y + 9 =0 and x-3y + 2 =0
so a1a2 + b1b2 = 2*1 + 6*(-3) = 2 – 18 = -16 <0

So negative sign will give me obtuse angle bisector

So
\frac{2x+6y + 9}{\sqrt{2^2 + 6^2}} = - \frac{(x-3y + 2 )}{\sqrt{1^2 + (-3)^2}}
Now you can simplify the above

Concept is SIGN OF a1a2 + b1b2 WILL GIVE ME THE EQUATION OF OBTUSE ANGLE BISECTOR

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