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.

x

_{1 }= 5, y_{1}= 3x

_{2 }= 3, y_{2}= -1By midpoint formula, x = (x

_{1}+x_{2})/2x = (5+3)/2 = 8/2 = 4

By midpoint formula, y = (y

_{1}+y_{2})/2y = (3+-1)/2 = 2/2 = 1

Hence the co-ordinates of M are (4,1).

By distance formula, d(AM) = √[(x

_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]x

_{1 }= 7, y_{1}= -3x

_{2 }= 4, y_{2}= 1d(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.