Let P = (-1, 0), Q = (0, 0) and R = (3, `3sqrt3`) be three points. The equation of the bisector of the angle PQR

Options

A. `(sqrt(3)//2)x+y= 0`
B. `x+sqrt(3)y= 0`
C. `sqrt(3)x+y= 0`
D. `x+(sqrt(3)//2)y= 0`

Answer

C

Explanation

The slope of QR is `(3sqrt(3)-0)//(3-0) = sqrt(3)`
`i.e., theta =60^(@)`
`"Clearly," anglePQR = 120^(@)`.
AQ is the angle bisector of the angle. So, line AQ makes `120^(@)` with the positive direction of the x-axis. Therefore, the equation of the bisector of `anglePQR` is
`y=x"tan" 120^(@) " or " y=-sqrt(3)x, i.e., sqrt(3)x+y=0`