Let $P = (-1, 0)$, $Q = (0, 0)$ and $R = (3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$

(B) $x + \frac{\sqrt{3}}{2}y = 0$

(C) $\frac{\sqrt{3}}{2}x + y = 0$

JEE Main · 2007 · 29 Apr 2007 · Offline · Straight Lines

Let

P = (- 1, 0)

Q = (0, 0)

and

R = (3, 33)

be three points. The equation of the bisector of the angle

P QR

(A) $3 x + y = 0$ ✓ Correct
(B) $x + \frac{3}{2} y = 0$
(C) $\frac{3}{2} x + y = 0$
(D) $x + 3 y = 0$

Answer: (A)

Solution

Place the angle at

Q = (0, 0)

. The ray

QP

points toward

(- 1, 0)

along the negative

x

-axis at angle

π

, while

QR

toward

(3, 33)

has slope

3

and makes angle

\frac{π}{3}

. The internal bisector lies at the mean direction

\frac{1}{2} (π + \frac{π}{3}) = \frac{2 π}{3}

, whose slope is

- 3

, giving the line

3 x + y = 0

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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