Mathematics: 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.

The answer is 7x - 3Step-by-step explanation:...

What are the coordinates of the centroid of a triangle

CameronVand21

15.03.2022

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:

$(x,y)=(\frac{x_{1}+x_{2}+x_{3}}{3}),(\frac{y_{1}+y_{2}+y_{3}}{3})$

Where,

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:

$(x,y)=(\frac{-4+2+2}{3},\frac{-1+2+(-3)}{3})\\(x,y)=(\frac{0}{3},\frac{-2}{3})\\(x,y)=(0,-\frac{2}{3})$

ANSWER: Coordinate of the Centroid of the Triangle $(0,-\frac{2}{3})$

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