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Question
The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the median AD
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Solution
Since AD is the median, D is the midpoint of BC.
∴ D ≡ `((2 - 1)/2, (0 + 6)/2) = (1/2, 3)`
∴ median AD passes through the points A(3, 4) and `"D"(1/2, 3)`.
∴ equation of the median AD is
`(y - 4)/(x - 3) = (3 - 4)/(1/2 - 3)`
= `(-1)/((-5/2)`
= `2/5`
∴ 5y – 20 = 2x – 6
∴ 2x – 5y + 14 = 0.
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