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Question
In ΔABC, A(3, 5), B(7, 8) and C(1, –10). Find the equation of the median through A.
Solution
The vertices of ΔABC are A(3, 5), B(7, 8) and C(1, –10).
Coordinates of the mid-point D of BC =
`((7 + 1)/2, (8 - 10)/2) = (8/2, (-2)/2) = (4, -1)`
Slope of AD = `(y_2 - y_1)/(x_2 - x_1)`
= `(-1 - 5)/(4 - 3)`
= `(-6)/1`
Slope of AD = – 6
Now, the equation of median AD is given by
y – y1 = m(x – x1)
∴ y – 5 = – 6(x – 3)
∴ y – 5 = – 6x + 18
∴ 6x + y – 5 – 18 = 0
∴ 6x + y – 23 = 0
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