Question

Find the lengths of the medians of a triangle whose vertices are A (-1, 3) and B (1, -1) and C (5, 1).

Answer 1

A (-1,3) B(1,-1) C(5,1)

>Median through A passes through A and midpoint of BC.
Midpoint of BC =

Length of Median =
Length of the median is 5 units.

>Median through B passes through B and midpoint of AC.
Midpoint of AC = $(\frac{5-1}{2},\frac{1+3}{2})=(2,2)$

Length of Median $=\sqrt{(2-1{)}^2+(2+1{)}^2}=\sqrt{10}$
Length of median is $\sqrt{10}$ units.

>Median through C passes through C and midpoint of AB.
Midpoint of BC =

Length of Median =
Length of the median is 5 units.