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

Back

21

Front

If ZX = 3 and X is the centroid, what is the length of AZ?

Back

9

Front

If DL = 24, what is the length of DG?

Back

8

Front

What type of segments are drawn from the centroid of a triangle?

Back

Medians.

Front

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

Back

The centroid (G) can be found using the formula: G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the relationship between the lengths of the segments created by the centroid on a median?

Back

The centroid divides the median into a ratio of 2:1, where the longer segment is twice the length of the shorter segment.

Front

If the length of a median is 30, what is the length of the segment from the vertex to the centroid?

Back

20

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle, where it would balance perfectly if made of a uniform material.