Question

Find the equations of the lines bisecting the angles between the line y=3x and the line y=x+3. Verify that the bisectors are perpendicular?

Answer 1

Proof is given below.

Explanation:

Slope of y= 3x is `m_1=` 3 and the slope of y= x+3 is `m_2`= 1. The interior angle between the lines would be given by

`tan theta=(m_2-m_1)/(1- m_1 m_2)` = `(1-3)/(1-3)`= 1. Hence `theta` would be 45 degrees and the exterior angle would be given by `(pi-theta)` =135 degrees

The bisector of interior angle would make an angle of 22`1/2` degrees and bisector of exterior angle would make an angle of 67`1/2` degrees with y=x+3. This implies that bisectors would be at right angles (22`1/2` +67`1/2= 90`) to each other.

Same situation would apply for the line y=3x.