Centroids

Front

What is a centroid?

Back

The centroid is the point where the three medians of a triangle intersect. It is also known as the center of mass or barycenter.

Front

If CP = 16, what is CL?

Back

CL = 24

Front

If BL = 12, what is BP?

Back

BP = 8

Front

If CP = 16, what is PL?

Back

PL = 8

Front

If AL = 27, what is AP?

Back

AP = 18

Front

If AZ = 24, what is AX?

Back

AX = 16

Front

What is the formula to find the centroid of a triangle given its vertices?

Back

The centroid (G) can be found using the formula G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3, where (x1, y1), (x2, y2), (x3, y3) are the coordinates of the vertices.

Front

What is the relationship between the centroid and the triangle's area?

Back

The centroid divides each median into two segments, one of which is twice the length of the other. The area of the triangle is divided into three smaller triangles of equal area by the medians.

Front

How does the centroid relate to the balance of a triangle?

Back

The centroid is the point at which a triangle can be balanced on the tip of a pencil, as it represents the average position of all the points in the triangle.

Front

What is the significance of the centroid in real-world applications?

Back

The centroid is used in various fields such as engineering, architecture, and physics to determine the center of mass and balance of structures.