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.



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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