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# 2D Coordinate Geometry

In the 1600s, René Descartes married algebra and geometry to create the Cartesian plane.

# Coordinate Geometry - Angle Bisector

Which of the following is one of the equations of the bisectors of the angles between \begin{align} 12x+3y+11 &= 0 \text{ and} \\ 3x-12y &= 0 ? \end{align}

Which of the following lines is a locus of equidistant points from the two lines \begin{align} 12x+5y+31 &= 0 \text{ and} \\ -5x+12y+3 &= 0 ? \end{align}

For the three points $$P=(-4,0),$$ $$Q=(0,0)$$ and $$R=(2,2\sqrt{3}),$$ what is the equation of the bisector of the angle $$\angle{PQR}?$$

Let $$\displaystyle y=-\frac{1}{\sqrt{5}}x$$ be one of the two bisectors of the angles between two lines $px+qy+r=0, p'x+q'y+r'=0$ which intersect at the point $$P=(-2\sqrt{5},2).$$ What is the $$y$$-intercept of the other bisector?

Let $$P=(-5,0)$$, $$Q=(0,0)$$ and $$R=(5,5\sqrt{3})$$ be three points on the $$xy$$-plane. Then what is the equation of the bisector of the angle $$\angle PQR ?$$

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