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 the center of mass of the triangle.

Front

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

Back

The length from the centroid to a vertex is 2/3 the length of the median from that vertex to the midpoint of the opposite side.

Front

If AZ = 24 and X is the centroid, what is AX?

Back

AX = 16.

Front

If BL = 12, what is BP if B is a vertex and P is the centroid?

Back

BP = 8.

Front

If DL = 24, what is DG?

Back

DG = 8.

Front

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

Back

AZ = 9.

Front

If G is the centroid of triangle ABC and BE = 18, what is BG?

Back

BG = 12.

Front

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

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

What is the formula for finding 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), and (x3, y3) are the coordinates of the vertices.

Front

What is the significance of the centroid in geometry?

Back

The centroid is significant as it represents the balance point of the triangle and is used in various applications in physics and engineering.