Question

the vertices of a triangle are A(1,3) B(5,7) C(11,13).Find the length of median passing through the vertex A

Answer 1

Vertices of the triangle
A = (1,3)
B = (5,7)
and 
C = (11,13)

Thus mid point D on BC
                                           D = (5+11/2,7+13/2)
                                           D = (8,10)
Thus coordinates of the median AD = (1,3) and (8,10)

Now calculating the length of median
                                   AD = root[ (8-1)^2 + (10-3)^2]
                                          = root [ 49 + 49]
                                          = 7 root 2
Thus length of median is 7 root 2