Properties of coordinates of centroid

Coordinates of centroid means centre of a closed figure or geometric centre of a plane figure described by coordinates. Here,  we have  seen two words: coordinates and centroid. Coordinates are the numbers which describe the position of a point in a particular space. The meaning of centroid is the centre of a closed figure e.g. triangle, cone, rectangle and square etc. in geometry,you can say  the word barycenter is the same as centroid. Centroid is a point in which a cutout of the shape could be balanced on a tip of a pin.

Properties of coordinates of centroid and centroid:

The properties of the coordinates of centroid and centroid are as follows –

• Coordinates of centroid tell us the position of the centre point of a closed geometric figure.
• It should always be inside the object.
• The centroid is the centre of the figure.
• It’s the point of concurrency of the mid.

Centroid of triangle and some figures:

The centroid is an important part of a triangle. With the help of triangle centroid and it’s  coordinates of centroid. We will understand the concept of coordinates of centroids . The triangle is of three types – Equilateral, Scalene and isosceles. The intersection point of the median of a triangle is it’s centroid or the meeting point of the median is the centroid of the triangle.

Centroid of any geometrical figure means it’s geometrical centre . So now we will see the centroid of some figures and after that we will find the coordinates of the it’s centroid . Let’s study the  centroid of a rectangle and square. The centroid of a rectangle  is the intersection point of its diagonal and also in square the centroid is the point where both the diagonals of  a square  intersect each other.

Centre of triangle other than the centroid:

Circle have four types of center –

1. CENTROID
2. THE CIRCUMCENTER
3. ORTHOCENTER
4. INCENTER

We have studied centroid and now we will know about the other three centres of the triangle.  

• THE CIRCUMCENTER:

The circumcenter is the middle of the circle such that every three vertices of the circle are the equal distance far  from the circumcenter. Thus, the circumcenter is the factor that forms the foundation of a circle wherein all three vertices of the triangle lie at the circle. Thus, the radius of the circle is the space among the circumcenter and any of the triangle’s three vertices. It is located via means of locating the midpoint of every leg of the triangle and building a line perpendicular to that leg at its midpoint. Where all 3 strains intersect is the circumcenter. The circumcenter is not always found in the interior part of the triangle.  In fact, it can be located  outside the triangle.

• ORTHOCENTER:

The orthocenter is the middle of the triangle made out of locating the altitudes of every side. The altitude of a triangle is created by means of losing a line from every vertex that is perpendicular to the other side. The altitude of the triangle is once in a while known as the height. Remember, the altitudes of a triangle do now no longer undergo the midpoints of the legs until you’ve got a unique triangle, like an equilateral triangle.

• INCENTER:

The incenter is the closing triangle middle we are able to investigate. It is the factor forming the starting place of a circle inscribed within the triangle. Like the centroid, the incenter is continually within the triangle. It is built with the aid of taking the intersection of the altitude bisectors of the three vertices of the triangle. The radius of the circle is acquired with the aid of losing a perpendicular from the incenter to any of the triangle legs.

Coordinates of centroid of triangle:

To find out the coordinates of centroid . find out the average of  x coordinate and y coordinate Where  X1 , X2 ,X3  are the x coordinates of the  triangle and Y1 ,  Y2 ,  Y3  are the y coordinates of a triangle. Centroid of a triangle contains X coordinates and Y coordinates.

To find out X coordinate-

(X1 + X2+ X3 )/ 3

To find out Y coordinates –

(Y1+Y2+Y3 ) / 3

Conclusion:

Coordinates of centroid  help us to locate the position of centroid . We can find out coordinates by finding  the average of X and Y coordinates  of three vertices of a triangle respectively . We also know about centroid which means centre position of any geometrical figure. There are also other centres which we have studied. Now we are  able to understand the coordinates of the centroid of the triangle. Coordinates play a very important role in mathematics. Without coordinates we are unable to find the centroid. To understand the concept of coordinates of centroid we have to learn about coordinates and centroid separately that is described above.