Question

Answer the following question:

The vertices of ∆PQR are P(2, 1), Q(−2, 3) and R(4, 5). Find the equation of the median through R.

Answer 1

Let S be the midpoint of side PQ.

Then RS is the median through R.

∴ S ≡ `((2 - 2)/2, (3 + 1)/2)` = (0, 2)

The median RS passes through the points R(4, 5) and S(0, 2).

∴ Equation of median RS is

`(y - 5)/(2 - 5) = (x - 4)/(0 - 4)`

∴ `(y - 5)/(-3) = (x - 4)/(-4)`

∴ 4(y – 5) = 3(x – 4)

∴ 4y – 20 = 3x – 12

∴ 3x – 4y + 8 = 0