Let P equiv (-3, 0),Q equiv (0, 0),and R equi | vedclass

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(C) The coordinates of the points are $P(-3, 0)$,$Q(0, 0)$,and $R(3, 3\sqrt{3})$.$QP$ lies along the negative $X$-axis,so the angle it makes with the

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$\sqrt{3} x + y = 0$

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(C) The coordinates of the points are $P(-3, 0)$,$Q(0, 0)$,and $R(3, 3\sqrt{3})$.$QP$ lies along the negative $X$-axis,so the angle it makes with the positive $X$-axis is $180^{\circ}$.The slope of $QR$ is $m = \frac{3\sqrt{3} - 0}{3 - 0} = \sqrt{3}$.Since $	an 	heta = \sqrt{3}$,the angle $	heta$ that $QR$ makes with the positive $X$-axis is $60^{\circ}$.The angle $\angle PQR$ is the angle between $QP$ and $QR$,which is $180^{\circ} - 60^{\circ} = 120^{\circ}$.The angle bisector of $\angle PQR$ divides this angle into two equal parts of $60^{\circ}$ each.The angle that the bisector makes with the positive $X$-axis is $180^{\circ} - 60^{\circ} = 120^{\circ}$.The slope of the bisector is $	an 120^{\circ} = -\sqrt{3}$.Since the bisector passes through the origin $Q(0, 0)$,its equation is $y - 0 = -\sqrt{3}(x - 0)$,which simplifies to $y = -\sqrt{3}x$ or $\sqrt{3}x + y = 0$.

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

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