Centroids

Front

What is a centroid in a triangle?

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

How do you find the length of a segment from the centroid to a vertex?

Back

The length from the centroid (G) to a vertex (A) is two-thirds the length of the median from that vertex to the midpoint of the opposite side.

Front

If the length of a median is 12, what is the length from the centroid to the vertex?

Back

8 (since the centroid divides the median in a 2:1 ratio).

Front

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

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

If the length of segment CP is 16, what is the length of segment CL?

Back

24 (since CL = 1.5 * CP).

Front

In triangle ABC, if X is the centroid and CW = 30, what is CX?

Back

20 (since CX = 2/3 * CW).

Front

If GF = 4 and G is the centroid of triangle ABC, what is the length of GC?

Back

8 (since GC = 2 * GF).

Front

If BX = 8, what is BY?

Back

12 (since BY = 1.5 * BX).

Front

If BL = 12, what is BP?

Back

8 (since BP = 2/3 * BL).

Front

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

Back

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