Question

Find the centroid of the triangle formed by the line 2x+3y-6=0 with the coordinate axes ​

Answer 1

Given line : 2x+3y-6=0

Therefore, y=2-(2/3)x

If x=0, then y= 2 and

If y=0, then x=3.

Hence the line cuts x axis at (3,0) and y axis at (0,2)

Third coordinate is origin (0,0)

Therefore, the triangle is formed by the points (0,2), (3,0) and (0,0)

Coordinates of the centroid are,

x=(0+0+3)/3 = 1

y=(2+0+0)/3 = 2/3

Ans: Centroid of the triangle is at (1, 2/3)