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प्रश्न
In ΔABC, A(3, 5), B(7, 8) and C(1, –10). Find the equation of the median through A.
उत्तर
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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