Find the length of the medians of the triangle whose vertices are (-1,3),(1,-1) and (5,1).

Let the given points of a triangle be A(-1, 3), B(1, -1) and C(5,1)

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

The coordinates of D are:

D = (3, 0)

The coordinates of E are:

E = (2, 2)

The coordinates of F are:

F = (0, 1)

Now, we have to find the lengths of the medians.

d(A,D) = √(x₂ – x₁)² + (y₂ – y₁)²

= √{3 – (-1)²} + {0 – 3}²

= √(3 + 1)² + (-3)²

= √16 + 9

= √25

= 5 units

d(B,E) = √(x₂ – x₁)² + (y₂ – y₁)²

= √(2 – 1)² + {2 – (-1)}²

= √(1)² + (2 + 1)²

= √1 + 9

= √10 units

d(C,F) = √(x₂ – x₁)² + (y₂ – y₁)²

= √(5 – 0)² + {1 – 1}²

= √(5)² + (0)²

= √25

= 5 units

Hence, the length of the medians AD, BE and CF are 5, √10, 5 units respectively.