Q. 85.0( 6 Votes )
The co-ordinates of vertices of A, B, C of a triangle ABC are (–1, 3), (1, –1) and (5, 1) respectively, let us calculate the length of Median AD.
Answer :
To calculate, the length of Median AD, first we’ll calculated the coordinates of mid-point 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 = 3 and y = 0
⇒ the coordinates of one end of median(x1, y1) = (– 1, 3) and of another end(x2, y2) = (3, 0).
Now, we know the length = √((x2 – x1)2 + (y2 – y1)2)
⇒ Length of median = √ ((3 –(– 1))2 + (0 – 3)2)
⇒ Length of median = √ (16 + 9)
⇒ Length of median = √ 25
⇒ Length of median = 5
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