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Geometry

2D Coordinate Geometry

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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