Question

Find the coordinates of the centroid P of the ΔABC, whose vertices are A(–1, 3), B(3, –1) and C(0, 0). Hence, find the equation of a line passing through P and parallel to AB.

Answer 1

By formula,

Centroid of triangle = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

Substituting values,, we get:

Centroid of △ABC = `((-1 + 3 + 0)/3, (3 + (-1) + 0)/3)`

P = `(2/3, 2/3)`

By formula,

Slope = `((y_2 - y_1)/(x_2 - x_1))`

= `(-4)/4`

= –1

We know that the slopes of parallel lines are equal.

By point-slope form,

Equation of line: y − y₁ = m(x − x₁)

Substituting values, we get:

Equation of line passing through P and parallel to AB:

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

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

3y − 2 = −1(3x − 2)

3y − 2 = −3x + 2

3y + 3x = 2 + 2

3x + 3y = 4