# Sample quiz on right bisectors Main home here.

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: $(3,1)$