Question

find the centoride of a triangle of sides x=0,y=0,x+y=9

Answer 1

see attachment,
we get three points 
  A ≡ (0,0)
  B ≡ (9,0)
  C ≡ (0,9)

we know,
if three points of triangle  (x₁,y₁) , (x₂,y₂ ) and (x₃, y₃) are given 
      then, centroid of triangle is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$
  
hence, 
centroid of ABC = {(0+9 + 0)/3,(0+ 0 + 9)/3 } = (3,3)

Answer 2

Heya User,

Given above are equations of three line....
---> x = 0 <--- [ The y - axis ]
---> y = 0 <--- [ The x - axis ]
---> x + y = 9 <--- ( i )

We'll need to find points of the triangle...
Sooo, a basic logic says ---> we've to find two points on the line -->
---> [ x + y = 9 ] such that one lies at x-axis and other at y

Soo, we frame two Simultaneous Systems for x = 0, Eqn (i) AND the second system as y = 0, Eqn (i) ....
--> Thus, we get the points as ( 0 , 9 ) , ( 9 , 0 )....

Given the Points, we apply the CENTROID Formula -->
--> $G(a,b) = [ \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} ]$
--> to get the points as ( 9/3 , 9/3 ) = ( 3,3 )

And hence, the Centroid of the Triangle is G ( 3,3 ).....