Question

find the coordinates of centroid of a triangle whose vertices are( 2,6) (8,12) (8,0)

Answer 1

Answer:

Answer is (6,6)

Step-by-step explanation:

Let the triangle having coordinates (x1,y1) (x2,y2) (x3,y3)

Here, they are (2,6) (8,12) (8,0)

The formulae for finding the centroid of a triangle when the vertices are given is

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

so,

( 2+8+8/3 , 6+12+9/3)

( 18/3 , 18/3 )

( 6,6 )

so this the centroid.....

Hope it helps.......

plz support me..

Answer 2

Given

Let coordinates of vertices be (X1,Y1), (X2,Y2), (X3,Y3)

and Vertices of centroid = (x, y)

Now,

• X1 = 2, Y1 = 6
• X2 = 8, Y2 = 12
• X3 = 8, Y3 = 0

To Find

• Coordinates of centroid( x,y ) = ?

Using Formula

For X,

$\large \boxed {\boxed {\tt \blue { x= \frac{x_{1} +x_{2} +x_{3} }{3} }}}$

For Y,

$\large \boxed {\boxed {\tt \blue { y = \frac{y_{1} +y_{2} +y_{3} }{3} }}}$

Solution

$\tt \implies \: x = \frac{x_{1} +x_{2} +x_{3} }{3} \\ \\ \tt \implies \: x = \frac{2 + 8 + 8}{3} \\ \\ \tt \implies x= \frac{18}{3} \\ \\ \tt \implies \: x = 6$

$\tt \implies \: y = \frac{y_{1} +y_{2} +y_{3} }{3} \\ \\ \tt \implies \:y = \frac{6 + 12 + 0}{3} \\ \\ \tt \implies \: y = \frac{18}{3} \\ \\ \tt \implies \: y = 6$

Coordinates of centroid = ( x,y ) = (6,6).

Hence, Coordinates of centroid are (6,6).