Q. 95.0( 8 Votes )

The co-ordinates of vertices of triangle are (2, –4), (6, –2) and (–4, 2) respectively. Let us find the length of three medians of triangle.

Answer :

The co-ordinates of vertices of a triangle ABC are A(2, – 4), B(6, –2) and C (– 4, 2) respectively.

To calculate, the length of Median AD, first we’ll calculated the coordinates of mid-point (d) of BC.


Let the coordinates of that mid-point be (x, y) –


And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x1, y1) and (x2, y2) is




x = 1 and y = 0


the coordinates of one end of median(x1, y1) = (2, – 4) and of another end(x2, y2) = (1, 0).


Now, we know the length = √ ((x2 – x1)2 + (y2 – y1)2)


Length of median = √ ((1 –(2))2 + (0 –(– 4))2)


Length of median = √ (1 + 16)


Length of median = √ 17


Now, to calculate, the length of Median BE, first we’ll calculated the coordinates of mid-point (E) of AC.


Let the coordinates of that mid-point be (x, y) –



x = – 1 and y = – 1


The coordinates of one end of median(x1, y1) = (6, – 2) and of another end(x2, y2) = (– 1, – 1).


Now, we know the length = √ ((x2 – x1)2 + (y2 – y1)2)


Length of median = √ ((– 1 –(6))2 + (– 1 –(– 2))2)


Length of median = √ (49 + 1)


Length of median = √ 50


And, now To calculate, the length of Median CG, first we’ll calculated the coordinates of mid-point (G) of AB.


Let the coordinates of that mid-point be (x, y) –



x = 4 and y = – 3


The coordinates of one end of median(x1, y1) = (– 4, 2) and of another end(x2, y2) = (4, – 3).


Now, we know the length)


Length of median


Length of median


Length of median


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