Question

A(1, 4), B(3, 2) and C(7, 5) are vertices of a triangle ABC. Find the equation of a line, through the centroid and parallel to AB.

Answer 1

Slope of the line parallel to AB = Slope of AB = −1

Thus, the required equation of the line is

y – y₁ = m(x – x₁)

`y - 11/3 = -1(x - 11/3)`

`y - 11/3 = -x + 11/3`

`y + x = 11/3 + 11/3`

`y + x = (11 + 11)/3`

= `22/3`

3y + 3x = 22