#### Equation for centroid

## How do you find the centroid?

To find the centroid of any triangle, construct line segments from the vertices of the interior angles of the triangle to the midpoints of their opposite sides. These line segments are the medians. Their intersection is the centroid.

## How is the centroid formula derived?

Derivation for the Formula of a Triangle’s Centroid (Proof) Let ABC be a triangle with the vertex coordinates A( (x_{1}, y_{1}), B(x_{2}, y_{2}), and C(x_{3}, y_{3}). The midpoints of the side BC, AB and AC are D, E, and F, respectively. The centroid of a triangle is represented as “G.”

## What is the centroid method?

The centroid method is an agglomerative clustering method, in which the similarities (or dissimilarities) among clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the variables being used in the clustering.

## What is centroid of triangle?

The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). The centroid divides each of the medians in the ratio 2:1, which is to say it is located ⅓ of the distance from each side to the opposite vertex (see figures at right).

## What is the centroid of an isosceles triangle?

An isosceles triangle is a triangle that has two sides of equal length. The centre of point of intersection of all the three medians in a triangle is the centroid.

## How do you find the centroid of a rectangle?

Centroid of rectangle is defined as the center point where all the diagonals intersect each other. The diagonals of the rectangle intersect at width b/2 from x – axis and at height h/2 from y – axis. It can also be termed as the geometric center.

## Where is the centroid of an equilateral triangle?

Centroid of an Equilateral Triangle The center of the circle is the centroid and height coincides with the median. The radius of the circumcircle is equal to two thirds the height.

## What is the difference between centroid and Centre of gravity?

The center of gravity of any object is termed to the point where gravity acts on the body. Where on the other hand, the centroid is referred to as the geometrical center of a uniform density object.

## What are the properties of centroid?

The properties of the centroid are as follows:The centroid is the centre of the object.It is the centre of gravity.It should always lie inside the object.It is the point of concurrency of the medians.

## Is centroid and Circumcenter the same?

The centroid is always between the orthocenter and the circumcenter. The distance between the centroid and the orthocenter is always twice the distance between the centroid and the circumcenter. In obtuse triangles, the circumcenter is always outside the triangle opposite the largest angle.

## What is centroid in civil engineering?

Centroid The point, at which the total area of a plane figure (such as rectangle, triangle, square, quadrilateral, circle etc) is assumed to be concentrated, is called the centroid of that area. The centroid is also represented by C.G. or G. The centroid and centre of gravity are at the same point.