Question

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

Answer 1

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