Question

A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle.

1) Find the coordinates of the centroid G of the triangle

2) Find the equation of the line through G and parallel to AC

Answer 1

Given vertices: A( 1, 3), B(4, 2) and C(3, 2)

1) Coordinates of the centroid G of ΔABC are given by

`G = ((-1+4+3)/3 , (3+2-2)/3) = (6/3, 3/3) = (2,1)`

2) Since the line through G is parallel to AC the slope of the lines are the same

`=> m = (y_2-y_1)/(x_2-x_1) = (-2-3)/(3-(-1)) = (-5)/4`

So, equation of the line passing throughG(2, 1) and with slopew `(-5)/4` is given by

`y - y_1 = m(x-x_1)`

`=> y - 1 = (-5)/4 (x - 2)`

`=> 4y - 4 = -5x + 10`

`=> 5x + 4y = 14` is the reuired equation.