Let the given points of a triangle be A(-1, 3), B(1, -1) and C(5,1)
Let D, E and F are the midpoints of the sides BC, CA and AB respectively.
The coordinates of D are:
F = (0, 1)
Now, we have to find the lengths of the medians.
d(A,D) = √(x2 – x1)2 + (y2 – y1)2
= √{3 – (-1)2} + {0 – 3}2
= √(3 + 1)2 + (-3)2
= √16 + 9
= √25
= 5 units
d(B,E) = √(x2 – x1)2 + (y2 – y1)2
= √(2 – 1)2 + {2 – (-1)}2
= √(1)2 + (2 + 1)2
= √1 + 9
= √10 units
d(C,F) = √(x2 – x1)2 + (y2 – y1)2
= √(5 – 0)2 + {1 – 1}2
= √(5)2 + (0)2
= √25
= 5 units
Hence, the length of the medians AD, BE and CF are 5, √10, 5 units respectively.
