Question

Find the coordinates of the centroid of the triangle whose sides lie along the lines$x=0,y=0$ and $3x+2y=12$ .

Answer 1

The sides of triangle are $x=0\cdots \left(1\right)y=0\cdots \left(2\right)3x+2y=12\cdots \left(3\right)$

point of intersection of $\left(1\right)\left(2\right)$ is $(0,0)$

Point of intersection of $\left(1\right)\left(3\right)$ is

$3\left(0\right)+2y=122y=12y=6$

$(x,y)=(0,6)$

Point of intersection of $\left(2\right)\left(3\right)$ is

$3x+2\left(0\right)=123x=12x=4$

$(x,y)=(4,0)$

So the vertices of triangle are $(0,0),(0,6),(4,0)$

Centroid is given as $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})(\frac{0+0+4}{3},\frac{0+6+0}{3})(\frac{4}{3},2)$