The coordinates of the centroid of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) are what?

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Multiple Choice

The coordinates of the centroid of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) are what?

The centroid sits at the average of the triangle’s vertex coordinates. If the vertices are (x1, y1), (x2, y2), and (x3, y3), its coordinates are ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3). Each vertex contributes equally to the centroid, so you average the x-coordinates and the y-coordinates separately. Dividing by 3 reflects averaging three points, not just two (which would give a midpoint of a side) or mixing divisors. This symmetric averaging ensures the point is the triangle’s balance point.

The centroid sits at the average of the triangle’s vertex coordinates. If the vertices are (x1, y1), (x2, y2), and (x3, y3), its coordinates are ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3). Each vertex contributes equally to the centroid, so you average the x-coordinates and the y-coordinates separately. Dividing by 3 reflects averaging three points, not just two (which would give a midpoint of a side) or mixing divisors. This symmetric averaging ensures the point is the triangle’s balance point.

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