# Sample quiz on median equations and lengths Main home here.

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 $A(0,0),~B(4,2),~C(2,6)$.
$(2,\frac{3}{8})$
$(2,\frac{8}{3})$
$(\frac{8}{3},2)$
$(\frac{3}{8},2)$.