ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10

Here a triangle ABC is given with their coordinates

You have to find the equation of the median through A.

This is the Question Number 23, Exercise 12.1 of M.L Aggarwal.

Deepak BoraNewbie

# In traingle ABC, A (3, 5), B (7, 8) and C (1, – 10). Find the equation of the median through A.

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Given,

∆ABC and their vertices A (3, 5), B (7, 8) and C (1, – 10).

And, AD is median

So, D is mid-point of BC

Hence, the co-ordinates of D is ([7 + 1]/2, [8 – 10]/2) = (4, -1)

Now,

Slope of AD, m = y

_{2}– y_{1}/ x_{2}– x_{1}m = (5 + 1)/ (3 – 4) = 6/-1 = -6

Thus, the equation of AD is given by

y – y

_{1}= m (x – x_{1})y + 1 = -6 (x – 4)

y + 1 = -6x + 24

⇒ 6x + y – 23 = 0