About Centroid Formula
The centroid refers to the object's geometric centre. The centroid formula is used to find the coordinates of the triangle's centroid. The point of intersection of all three triangle medians can be used to establish the triangle's centroid. The triangle's centroid divides all of the medians in a 2:1 ratio. Let's look at the centroid formula and solve a few cases at the end.
What Is a Centroid Formula?
The centre of a triangle is known as the centroid. It's known as the triangle's point of convergence of medians.
Centroid Formula
The centroid formula for a given triangle is as follows:
C =((x1+x2+x3) / 3,(y1+y2+y3) / 3)
where,
- C denotes the centroid of a triangle
- x1,x2,x3 are the x-coordinates of the 3 vertices.
- y1,y2,y3are the y-coordinates of the 3 vertices.
Derivation of Centroid Formula
To find the centroid of a triangle, we use the section formula. Let PQR be any triangle with vertices P(x1, y1), Q(x2,y2), and R(x3,y3), and D, E, and F, respectively, be the midpoints of the sides PQ, QR, and PR. The centroid of a triangle is denoted by the letter G. Because D is the midpoint of side PQ, we can calculate its coordinates using the midpoint formula.,Since, D is the midpoint of side PQ, applying the midpoint formula, we get its coordinates as,
D((x1+x2)/2)
The triangle's centroid separates the medians in a 2:1 ratio. As a result, we can find the coordinates of G using the coordinates of D.
X-coordinate of G: [(2(x1+x2)/2)+ 1(x3)]/(2+1) = (x1+x2+x3)/3
Y-coordinate of G:[(2(y1+y2)/2)+ 1(y3)]/(2+1) = (y1+y2+y3)/3
Therefore, the coordinates of G are given as, ((x1+x2+x3)/3,(y1+y2+y3)/3). To get all the Maths formulas check out the main page.
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