Q. 285.0( 3 Votes )

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

Answer :

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


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