Here given vertices of triangle are A (-1, 3), B (1, -1) and C (5, 1).

Let D, E and F be the midpoints of the sides BC, CA and AB respectively.

We need to find length of median passing through A, ie distance between AD.

Let point D ≡ (x, y)

By midpoint formula,

x = , y =

For midpoint D of side BC,

x = , y =

∴ x = , y =

∴D(x , y) ≡ (3, 0 )

Now, by distance formula,

XY =

For AD,

AD =

∴ AD =

AD =

∴AD = 5 units

Hence, the length of the median through A is 5 units