Question

The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the midpoints of sides AB and BC

Answer 1

Let P, Q be the midpoints of sides AB and BC respectively.

Then P ≡ `((3 + 2)/2, (4 + 0)/2) = (5/2, 2)`

and Q ≡ `((2 - 1)/2, (0 + 6)/2) = (1/2, 3)`

∴ equation of the required line, i.e., line PQ is

`(y - 2)/(x - 5/2) = (3 - 2)/(1/2 - 5/2)`

∴ `(2y - 4)/(2x - 5) = 1/(-2)`

∴ – 4y + 8 = 2x – 5

∴ 2x + 4y –  13 = 0.