Question

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

Enter your answers in the boxes. ( , )

Answer 1

(0,-0.6667)

Step-by-step explanation:

Centroid = ((x1 + x2 + x3)/3, (y1 + y2 + x3)/3)

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

= (0/3, -2/3)

= (0, -0.6667)

Answer 2

Answer: The centroid of the triangle PQR is
`(0,(-2)/(3) )`.

Step-by-step explanation:

It is given that the vertices of the triangle are P(−4, −1) , Q(2, 2) , and R(2, −3).

The formula to find the coordinates of the centroid of a triangle is,

`\text{coordinates of centroid}=((x_1+x_2+x_3)/(3) ,(y_1+y_2+y_3)/(3) )`

We have coordinates of all vertices, so we can directly substitute the values in the above mentioned formula.

`\text{coordinates of centroid}=((-4+2+2)/(3) ,(-1+2+(-3))/(3) )`

`\text{coordinates of centroid}=((0)/(3) ,(-2)/(3) )`

`\text{coordinates of centroid}=(0,(-2)/(3) )`

Therefore the coordinates of the centroid of a triangle PQR is
`(0,(-2)/(3) )`.