Summary
This math recipe will help you find the centroid of a triangle, coordinates of whose vertices are known.
Skill Level
Easy
Time
Approx. 2 min
Ingredients
Coordinates of the three vertices: \(A(x_1, y_1)\), \(B(x_2, y_2)\), and \(C(x_3, y_3)\)
Method
To find the centroid \(G\) of \(\Delta ABC\), we’ll simply plug their coordinates into the formula below:
\(G \equiv \left ( \frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3} \right ) \)
This formula is sometimes called the Centroid Formula.
Examples
Example 1 Find the centroid of the triangle, whose vertices are \(P(4, 6)\), \(Q(-2, 2)\), and \(R(1, 1)\).
Solution The figure shows \(\Delta PQR\) on the plane.
To find the centroid \(G\), we’ll use the centroid formula directly.
\(G \equiv \left ( \frac{4+(-2)+1}{3},\frac{6+2+1}{3} \right ) \)
\( \equiv \left ( \frac{3}{3},\frac{9}{3} \right ) \)
\( \equiv (1,3) \)
Example 2 Find the centroid of the triangle, whose vertices are \(A(-1, 5)\), \(B(7, -3)\), and \(C(0, 2)\).
Solution The figure shows \(\Delta ABC\) on the plane.
To find the centroid \(G\), we’ll again use the centroid formula.
\(G \equiv \left ( \frac{-1+7+0}{3},\frac{5+(-3)+(-2)}{3} \right ) \)
\( \equiv \left ( \frac{6}{3},\frac{0}{3} \right ) \)
\( \equiv (2,0) \)
That’s it for this recipe. Hope you found it helpful.
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