Question

What are the coordinates of the centroid of a triangle with vertices A(−3, 1) , B(1, 6) , and C(5, 2) ?

Answer 1

`O(1,3)`

Explanation:

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The centroid of a triangle is where the three medians of it intersect. The centroid divides each median into two segments that have a ratio of `2` to `1`.

The coordinates of the centroid `O` can be calculated using the following formulas:

`O_x=(A_x+B_x+C_x)/3` and

`O_y=(A_y+B_y+C_y)/3`

where `O_x` and `O_y` are the `x` and `y` coordinates of the centroid and `A_x` and `A_y` are `x` and `y` coordinates of the vertex `A`, and so on.

`O_x=(-3+1+5)/3=1`

`O_y=(1+6+2)/3=3`

`O(1,3)`