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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 median AD.
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Solution
Vertices of ΔABC are A(3, 4), B(2, 0) and C(1, 6)
Let D be the midpoint of side BC.
Then, AD is the median through A.
∴ D = `((2 + 1)/2, (0 + 6)/2) = (3/2, 3)`
The median AD passes through the points
A(3, 4) and `"D"(3/2, 3)`
∴ The equation of the median AD is
`(y - 4)/(3 - 4) = (x - 3)/(3/2 - 3)`
∴ `(y - 4)/(-1) = (x - 3)/(-3/2)`
∴ `3/2 (y - 4)` = x – 3
∴ 3y – 12 = 2x – 6
∴ 2x – 3y + 6 = 0
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