Question

What are the coordinates of the centroid of a triangle with vertices A(−3, 1) , B(1, 6) , and C(5, 2) ?

Answer 1

The centroid is the average of all the coordinates.
-3+1+5/2=x
x=3/3
1+6+2/2=y
y=9/3
The answer is (1,3)

Answer 2

Answer: (1,3)

Step-by-step explanation:

the centroid is point inside a triangle where center of all three sides lies.

we have formula for centroid as
`(x,y)=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3) )`

here we have three coordinates of both variables x, y are given as below

`x_1= -3, x_2=1, x_3=5\\y_1=1, y_2=6, y_3=2`

substituting the values of given variables in the formula we will get

`x =(-3+1+5)/(3) =1\\\\y =(1+6+2)/(3)=3`

Hence, centroid of given triangle ABC is (x,y) = (1,3)