M.L Aggarwal book Important Question of class 10 chapter Based on Section Formula for ICSE BOARD.
You have to Calculate the length of the median through the vertex A of the triangle ABC with given vertices in the question.
This is the Question Number 22, Exercise 11 of M.L Aggarwal.
Deepak BoraNewbie
Calculate the length of the median through the vertex A of the triangle ABC with vertices A (7, – 3), B (5, 3) and C (3, – 1).
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Let M(x,y) be the median of ΔABC through A to BC.
M will be the midpoint of BC.
x1 = 5, y1 = 3
x2 = 3, y2 = -1
By midpoint formula, x = (x1+x2)/2
x = (5+3)/2 = 8/2 = 4
By midpoint formula, y = (y1+y2)/2
y = (3+-1)/2 = 2/2 = 1
Hence the co-ordinates of M are (4,1).
By distance formula, d(AM) = √[(x2-x1)2+(y2-y1)2]
x1 = 7, y1 = -3
x2 = 4, y2 = 1
d(AM) = √[(4-7)2+(1-(-3))2]
d(AM) = √[(-3)2+(4)2]
d(AM) = √(9+16)
d(AM) = √25 = 5
Hence the length of the median AM is 5 units.