Find the lengths of the medians of a ABC having vertices at A (0,-1), B (2, 1) and C (0, 3).

Here given vertices are A (0,-1), B (2, 1) and C (0, 3) and let midpoints of BC, CA and AB be D,E and F respectively.

By midpoint formula.

x = , y =

For midpoint D of side BC,

x = , y =

x = , y =

∴midpoint of side BC is D(1, 2)

For midpoint E of side AB,

x = , y =

x = , y =

∴midpoint of side AB is E(0, 1)

For midpoint F of side CA,

x = , y =

x = , y =

∴midpoint of side CA is F(1, 0)

By distance formula,

XY =

For median AD,

AD =

=

= units

For median BE,

BE =

=

= 2 units.

For median CF,

CF =

=

= units