Question

the centroid of a triangle whose vertices are (2,3),(X,Y),(3,-2) is (0,0)then find (X, Y)

Answer 1

the centroid of triangle formula are
x=(x1+x2+x3) /3
0 =( 2+x+3)/3
0=x+5
x=-5
y=(y1+y2+y3) /3
0=( 3+y+(-2)) /3
0= y+1
or y=-1

Answer 2

The point (x, y) = (-5, -1)

Given:

Triangle vertices are (2,3), (x,y) and (3,-2)

The centroid of the triangle = (0, 0)

To find:

The value of (x, y)

Solution:

As we know the formula for the centroid of a triangle whose vertices are (x₁, y₁) (x₂, y₂) and (x₃, y₃) is given by  

⇒ Centroid = ( (x₁+x₂+x₃)/3 ,   (y₁+y₂+y₃)/3)  

By using above formula find the the centroid of a triangle whose vertices are (2,3), (x,y) and (3,-2)

⇒ cantroid  = ( 2+x+3/3 ,   3+y-2/3)

= ( 5+x/ 3 , 1+y/3 )

From given data centroid of data = (0, 0)

⇒ ( 5+x/ 3 , 1+y/3 ) = (0, 0)

⇒ 5+x/ 3 = 0        and    1+y/3 = 0

   5+ x = 0                      1+y = 0

         x = -5                       y = -1

Therefore, The point (x, y) = (-5, -1)

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