Question

What are the coordinates of the centroid of a triangle with vertices P(−4, −1) , Q(2, 2) , and R(2, −3) ?

Answer 1

the centroid is: x=0, y = -2/3

Answer 2

`(x,y)=(0,(-2)/(3))`

Explanation:

Given : Vertices of Triangle
`P(x_1,y_1)=(-4,-1)` ,
`Q(x_2,y_2)=(2, 2)` and
`R(x_3,y_3)=(2,-3)`

To find : Centroid of a triangle

The centroid of a triangle is the point of intersection of the three medians of the triangle.

The formula to calculate the centroid of a triangle is:

`(x,y)=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3))`

Where,
`x_1,x_2,x_3,y_1,y_2,y_3` are the coordinates of the centroid

Substituting the values in the formula gives us:

`(x,y)=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3))`

`(x,y)=((-4+2+2)/(3),(-1+2-3)/(3))`

`(x,y)=((0)/(3),(-2)/(3))`

Therefore,
`(x,y)=(0,(-2)/(3))`