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Deepak Bora
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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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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.

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  1. ML Aggarwal Solutions for Class 10 Chapter 12 - 5

    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 = y2 – y1/ x2 – x1

    m = (5 + 1)/ (3 – 4) = 6/-1 = -6

    Thus, the equation of AD is given by

    y – y1 = m (x – x1)

    y + 1 = -6 (x – 4)

    y + 1 = -6x + 24

    ⇒ 6x + y – 23 = 0

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