How can i find the centroid of a triangle

Therefore, from the coordinates of D, we can find the coordinates of G as,. Let us have a look at a few solved examples to understand the centroid formula better. Example 1: Vertices of the triangle are 4,3 , 6,5 , and 5,4. Determine the centroid of a triangle using the centroid formula.

Example 2: If the coordinates of the centroid of a triangle are 3, 3 and the vertices of the triangle are 1, 5 , -1, 1 , and k, 3 , then find the value of k. Example 3: Calculate the centroid of a triangle with vertices 1,3 , 2,1 , and 3,2. The centroid formula is the formula used for the calculation of the centroid of a triangle. Centroid is the geometric center of any object. The centroid of a triangle refers to that point that divides the medians in We can derive the centroid of a triangle formula using the section formula.

Before understanding the point of concurrency, let us discuss the medians of a triangle. Medians are the line segments that are drawn from the vertex to the mid-point of the opposite side of the vertex.

Each median of a triangle divides the triangle into two smaller triangles that have equal areas. The point of intersection of the medians of a triangle is known as centroid.

The centroid always lies inside a triangle, unlike other points of concurrencies of a triangle. Let us learn more about the centroid of a triangle along with a few solved examples and practice questions. The centroid of a triangle is formed when three medians of a triangle intersect. It is one of the four points of concurrencies of a triangle. The medians of a triangle are constructed when the vertices of a triangle are joined with the midpoint of the opposite sides of the triangle.

Observe the following figure that shows the centroid of a triangle. The following points show the properties of the centroid of a triangle which are very helpful to distinguish the centroid from all the other points of concurrencies. The centroid of a triangle formula is used to find the centroid of a triangle uses the coordinates of the vertices of a triangle.

The coordinates of the centroid of a triangle can only be calculated if we know the coordinates of the vertices of the triangle. The formula for the centroid of the triangle is:. Observe the following figure which shows the vertices of the triangle in the form of coordinates. There are various types of differences between the orthocenter and the centroid of the triangle. Recall that the centroid of a triangle is the point where the triangle's three medians intersect.

It is also the center of gravity of the triangle. For more see Centroid of a triangle. The coordinates of the centroid are simply the average of the coordinates of the vertices. So to find the x coordinate of the orthocenter, add up the three vertex x coordinates and divide by three.