+0

# What are the coordinates of the centroid of a triangle with vertices J(−4, 2) , K(2, 4) , and L(0, −2) ?

+1
756
2
+1016

What are the coordinates of the centroid of a triangle with vertices J(−4, 2) , K(2, 4) , and L(0, −2) ?

Nov 4, 2017

#1
+96189
+1

Find the midpoint of the side with  (2,4)  and ( -4,2) as vertexes  =

(  [ 2 + -4 ] / 2,  [ 2 + 4 ] / 2 )  =  (-1, 3)

Find the point 2/3 of the distance from (0,-2) to (-1,3)  =

(0 + (-1 - 0) (2/3) , -2 + ( 3 - -2)(2/3)  )

( 0  - 2/3,  -2 + (5)(2/3)  )

(-2/3, -2 +10/3 )

(-2/3 , 4/3 )   and this is the centroid....

Nov 5, 2017

#1
+96189
+1

Find the midpoint of the side with  (2,4)  and ( -4,2) as vertexes  =

(  [ 2 + -4 ] / 2,  [ 2 + 4 ] / 2 )  =  (-1, 3)

Find the point 2/3 of the distance from (0,-2) to (-1,3)  =

(0 + (-1 - 0) (2/3) , -2 + ( 3 - -2)(2/3)  )

( 0  - 2/3,  -2 + (5)(2/3)  )

(-2/3, -2 +10/3 )

(-2/3 , 4/3 )   and this is the centroid....

CPhill Nov 5, 2017
#2
+96189
+1

Centroid  =

(  Add the x coordinates of the vertices / 3, add the y coordinates of the vertices / 3  )

So we have

( [ -4 + 2 + 0] / 3 , [ 2 +  4 +  -2 ] / 3 )  \

[ -2/3,  4/3 ]

Nov 5, 2017