Median & Centroid

Front

What is the centroid of a triangle?

Back

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

Front

How does the centroid divide each median of a triangle?

Back

The centroid divides each median into two segments, with the shorter segment being one third the length of the entire median.

Front

If AG is 16, what is the length of GD?

Back

8 (Since G is the centroid, GD is one half of AG).

Front

If G is the centroid and GE = 7, what is the length of BE?

Back

21 (BE is twice the length of GE).

Front

What is the point of concurrency for the medians of a triangle?

Back

Centroid.

Front

If BE = 18, what is the length of BG?

Back

12 (BG is two thirds of BE).

Front

What is the relationship between the centroid and the area of a triangle?

Back

The centroid divides the triangle into three smaller triangles of equal area.

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex of the triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the formula to find the centroid of a triangle with vertices at (x1, y1), (x2, y2), (x3, y3)?

Back

Centroid (G) = ((x1+x2+x3)/3, (y1+y2+y3)/3).