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.

Answer 1

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