Q. 74.0( 4 Votes )

Find the lengths of the medians AD and BE of ΔABC whose vertices are A(7, -3), B(5, 3) and C(3, -1).

Answer :

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.


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fig.4


Mid-point of side BC opposite to vertex A i.e. coordinates of point D is given by-




= (4,1)


Mid-point of side AC opposite to vertex B i.e. coordinates of point E is given by-




= (5,-2)


Length of Median AD is given by-




= √(9 + 16)


= √25


= 5 units


Length of Median BE is given by-




= √(0 + 52 )


= √25


= 5 units


Thus, Length of Medians AD and BE are same which is equal to 5 units.


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