Centroid of a triangle is the common point through which all the three medians of the triangle pass. This common point or centroid where all the medians meet, divide each median in the ratio of 2:1. Centroid plays an important role of dividing a triangle into equal parts. This article on how to calculate centroid will help you in calculating the centroid for a triangle using a formula.
If you want to locate a centroid of a triangle, then draw medians from each vertex of the triangle on the opposite side. A median is a perpendicular bisector of the side of the triangle drawn from its vertex. The point of contact of all the medians is the centroid of the triangle
Calculating centroid of a triangle
The centroid of a triangle is given by the formula:
Where,
(x1, y1), (x2, y2), (x3, y3) are the coordinates of the triangle.
- You can easily find out the centroid of a triangle if the coordinates of a triangle are given. Just place the values of the given coordinates in the above formula and solve the equation. The values of x and y coordinates which you get after solving the equation is the centroid of the triangle.
- If you are not given the values of x and y coordinates of the vertices, but the triangle is given to then you need to draw the Cartesian coordinates around the triangle and determine the centroid of the triangle.
- While drawing the Cartesian coordinates around the triangle, choose one of the vertices of the triangle as the origin and draw one line intersecting that vertex as the positive x-axis. Draw all the other lines of the Cartesian system.
- Now, note down the coordinates of other vertices of the triangle. The vertex chosen as origin will have the coordinates (0, 0), the second vertex will be (a, 0) and the other vertex will be (b, c).
- You can now place the values of the vertices or x and y coordinates in the above formula and find the centroid of the triangle or calculate x coordinate using the formula (0+a+b)/3 and y coordinate using the formula (0+0+c)/3 or c/3.
- Sometimes you are given the triangle drawn on the graph paper or on the Cartesian system, in such case you just have to find the coordinates and place the values in the formula to find the centroid.
Example for calculating centroid
Suppose we want to find centroid of a triangle whose vertices are given as (2, 3), (-1, -3) and (3, 4).
Now,
- x1 = 2, y1 = 3,
- x2 = -1, y2 = -3 and
- x3 = 3, y3 = – 4
Using the formula for calculating centroid
X coordinate of centroid = ( x1 + x2 + x3)/3
= (2+ (-1) +3)/3
= 5
Y coordinate of centroid = (y1 + y2 + y3)
= (3+ (-3) + (-4))
= – 4
Therefore, coordinates of centroid of a triangle or centroid of a triangle are (5, -4).
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