Find the lengths of the medians of a ABC having vertices at A (5, 1), B (1, 5), and C(-3, -1).
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(1, 0)
For midpoint F of side CA,
x = , y =
x = , y =
∴midpoint of side CA is F(3, 3)
By distance formula,
XY =
For median AD,
AD =
=
= units
For median BE,
BE =
=
= 5 units.
For median CF,
CF =
=
= units