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Let P=(-1, 0), Q=(0,0) and R=(3, 3sqrt3)...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
C

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`
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