Sample quiz on right bisectors
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1. $\triangle ABC$ has vertices at $A(-4,1),~B(2,-2),~C(5,7)$. Find the equation of the right bisector of side $AB$.
   
   A: $y=2x+\frac{3}{2}$
   B: $y=2x-\frac{3}{2}$
   C: $y=2x-\frac{5}{2}$
   D: $y=-\frac{1}{2}x+\frac{3}{2}$
   
2. $\triangle ABC$ has vertices at $A(-4,1),~B(2,-2),~C(5,7)$. Find the equation of the right bisector of side $BC$
   
   A: $y=3x+\frac{11}{3}$
   B: $y=-\frac{1}{3}x-\frac{11}{3}$
   C: $y=-\frac{1}{3}x+\frac{11}{3}$
   D: $y=\frac{7}{2}x+\frac{5}{2}$
3. $\triangle ABC$ has vertices at $A(-4,1),~B(2,-2),~C(5,7)$. Find the equation of the right bisector of side $CA$.
   
   A: $y=-\frac{2}{3}x+\frac{19}{4}$
   B: $y=-\frac{3}{2}x-\frac{19}{4}$
   C: $y=-\frac{3}{2}x-\frac{13}{4}$
   D: $y=-\frac{3}{2}x+\frac{19}{4}$
4. Find the coordinates of the circumcenter of $\triangle ABC$ with vertices at $A(-4,1),~B(2,-2),~C(5,7)$.
   
   A: $\Big(\frac{13}{14},\frac{47}{14}\Big)$
   B: $\Big(\frac{47}{14},\frac{13}{14}\Big)$
   C: $\Big(\frac{13}{14},\frac{29}{16}\Big)$
   D: $\Big(\frac{13}{14},\frac{16}{9}\Big)$
5. $\triangle ABC$ has vertices at $A(-1,1),~B(1,-2),~C(4,2)$. Find the equation of the right bisector of $AB$.
   
   A: $y=-\frac{2}{3}x-\frac{1}{2}$
   B: $y=-\frac{3}{2}x-\frac{1}{2}$
   C: $y=\frac{2}{3}x-\frac{1}{2}$
   D: $y=\frac{2}{3}x+\frac{1}{2}$
6. $\triangle ABC$ has vertices at $A(-1,1),~B(1,-2),~C(4,2)$. Find the equation of the right bisector of $BC$.
   
   A: $y=-\frac{3}{4}x-\frac{15}{2}$
   B: $y=-\frac{3}{4}x+\frac{15}{8}$
   C: $y=\frac{4}{3}x+\frac{15}{2}$
   D: $y=\frac{4}{3}x-\frac{15}{2}$
7. $\triangle ABC$ has vertices at $A(-1,1),~B(1,-2),~C(4,2)$. Find the equation of the right bisector of $CA$.
   
   A: $y=\frac{1}{5}x+9$
   B: $y=\frac{1}{5}x-9$
   C: $y=-5x+9$
   D: $y=-5x-9$
8. Find the circumcenter of $\triangle ABC$ whose vertices are located at $A(-1,1),~B(1,-2),~C(4,2)$.
   
   A: $\Big(\frac{21}{34},\frac{57}{34}\Big)$
   B: $\Big(\frac{57}{34},\frac{21}{34}\Big)$
   C: $\Big(\frac{57}{34},-\frac{21}{34}\Big)$
   D: $\Big(\frac{21}{34},-\frac{57}{34}\Big)$
9. Find the center of a circle which goes through the points $(-2,0),~(2,2),~(3,0)$.
   
   A: $(\frac{1}{2},0)$
   B: $(0,\frac{1}{2})$
   C: $(-\frac{1}{2},0)$
   D: $(0,-\frac{1}{2})$
10. Find the center of a circle which goes through the points $(-1,2),~(2,-3),~(7,0)$.
    
    A: $(-1,3)$
    B: $(-3,1)$
    C: $(1,3)$
    D: $(3,1)$