Find the lengths of the medians AD and BE of ΔABC whose vertices are A(7, -3), B(5, 3) and C(3, -1).
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
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.