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

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 2

The centroid of a triangle is the point of intersection of the 3 medians of the triangle.

A median of a triangle is the line that goes from one vertex to the midpoint of the opposite side of the triangle.

*** In the attached image, lines BE, CF, and AD are the medians & point G is the centroid. ***

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,y)` are the coordinates of the centroid
• 
  `(x_(1),y_(1)),(x_(2),y_(2)), AND (x_(3),y_(3))` are the 3 vertices of the triangle

Using the 3 points
`P(-4,-1), Q(2,2), R(2,-3)` and substituting in the formula gives us:

`(x,y)=((-4+2+2)/(3),(-1+2+(-3))/(3))\\(x,y)=((0)/(3),(-2)/(3))\\(x,y)=(0,-(2)/(3))`

ANSWER: Coordinate of the Centroid of the Triangle
`(0,-(2)/(3))`