What is the centroid of a triangle with corners at $(3, 2 )$ , $(5,5 )$ , and $(12 , 9 )$ ?

Question

What is the centroid of a triangle with corners at $(5, 1)$ , $(4, 9)$ , and $(7,2)$ ?
What is the centroid of a triangle with corners at $(5, 2 )$ , $(2, 5)$ , and $(7,2)$ ?
What is the centroid of a triangle with corners at $(5, 2 )$ , $(2, 5 )$ , and $(5,3 )$ ?
What is the centroid of a triangle with corners at $(1, 4 )$ , $(3, 5 )$ , and $(5,3 )$ ?
What is the centroid of a triangle with corners at $(1, 1 )$ , $(3, 2 )$ , and $(8 , 6 )$ ?
What is the centroid of a triangle with corners at $(6, 1 )$ , $(2, 2 )$ , and $(1 , 6 )$ ?
What is the centroid of a triangle with corners at $(3, 1 )$ , $(5, 2 )$ , and $(12 , 6 )$ ?
What is the centroid of a triangle with corners at $(3, 2 )$ , $(1,5 )$ , and $(0 , 9 )$ ?
What is the centroid of a triangle with corners at $(2, 7 )$ , $(1,5 )$ , and $(7 , 5 )$ ?
What is the centroid of a triangle with corners at $(4, 7 )$ , $(1,2 )$ , and $(8 , 5 )$ ?

2286 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-16T17:34:24

The centroid $= (20)/3 , (16)/3$

The corners of the triangle are
$(3,2) = color(blue)(x_1,y_1$
$(5,5) = color(blue)(x_2,y_2$
$(12,9) = color(blue)(x_3,y_3$

The centroid is found using formula

centroid $= (x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3$

$= (3+5+12)/3 , (2+5+9)/3$

$= (20)/3 , (16)/3$

What is the centroid of a triangle with corners at (3, 2 )(3, 2 ), (5,5 )(5,5 ), and (12 , 9 )(12 , 9 )?