Sample quiz on median equations and lengths
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1. A triangle has vertices at $A(0,0),~B(4,2),~C(2,6)$. Find the equation of the median through $C$.
   
   $y=2x$
   $y=2$
   $x=2$
   $x=2y$
   
2. $\triangle ABC$ has vertices at $A(0,0),~B(4,2),~C(2,6)$. Find the length of the median through $C$.
   
   $5$
   $7$
   $\sqrt{5}$
   $\sqrt{7}$
3. $\triangle ABC$ has vertices at $A(-3,1),~B(2,3),~C(1,-1)$. Find the equation of the median through $B$.
   
   $y=-x-1$
   $y=-x+1$
   $y=x-1$
   $y=x+1$
4. $\triangle ABC$ has vertices at $A(-3,1),~B(2,3),~C(1,-1)$. Find the length of the median through $B$.
   
   $2\sqrt{3}$
   $3\sqrt{2}$
   $\sqrt{10}$
   $\sqrt{6}$
5. $\triangle ABC$ has vertices at $A(-3,1),~B(2,3),~C(1,-1)$. Which median is parallel to the line $y=-2x-11$?
   
   Median through $A$
   Median through $B$
   Median through $C$
   None of the above.
6. $\triangle PQR$ has vertices at $P(4,1),~Q(2,-2),~R(-2,2)$. Find the equation of the median through $P$.
   
   $y=\frac{x}{4}$
   $y=4x$
   $y=1$
   $x=4$
7. $\triangle PQR$ has vertices at $P(4,1),~Q(2,-2),~R(-2,2)$. Find the length of the median through $P$.
   
   $3$
   $17$
   $\sqrt{17}$
   $\sqrt{15}$
8. $\triangle PQR$ has vertices at $P(4,1),~Q(2,-2),~R(-2,2)$. Which median is perpendicular to $y=\frac{2x}{9}+\frac{5}{9}$?
   
   Through $P$
   Through $Q$
   Through $R$
   None of the above
9. Find the coordinates of the centroid of $\triangle PQR$ whose vertices are located at $P(4,1),~Q(2,-2),~R(-2,2)$
   
   $(\frac{4}{3},\frac{1}{3})$
   $(\frac{1}{3},\frac{4}{3})$
   $(\frac{3}{4},\frac{1}{3})$
   $(\frac{1}{3},\frac{1}{3})$
10. Find the coordinates of the centroid of $\triangle ABC$ with vertices at $A(0,0),~B(4,2),~C(2,6)$.
    
    $(2,\frac{3}{8})$
    $(2,\frac{8}{3})$
    $(\frac{8}{3},2)$
    $(\frac{3}{8},2)$.