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Question
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the medians.
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Solution
Let D, E, and F be the midpoints of sides BC, AC, and AB respectively of ΔABC.
Then D ≡ `((2 + 1)/2, (3 + 6)/2) = (3/2, 9/2)`
E ≡ `((1 + 1)/2, (6 + 4)/2)` = (1, 5)
F ≡ `((1 + 2)/2, (4 + 3)/2) = (3/2, 7/2)`
Equation of median AD is
`(y - 4)/(9/2 - 4) = (x - 1)/(3/2 - 1)`
∴ `(y - 4)/(1/2) = (x - 1)/(1/2)`
∴ x – y + 3 = 0
Equation of median BE is
`(y - 3)/(5 - 3) = (x - 2)/(1 - 2)`
∴ – 1(y – 3) = 2(x – 2)
∴ – y + 3 = 2x – 4
∴ 2x + y = 7
Equation of median CF is
`(y - 6)/(7/2 - 6) = (x - 1)/(3/2 - 1)`
∴ `(y - 6)/(-5/2) = (x - 1)/(1/2)`
∴ y – 6 = – 5(x – 1)
∴ 5x + y – 11 = 0
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