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 is the centroid related to the medians of a triangle?

Back

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

Front

If AG is the median of triangle ABC and G is the centroid, what is the relationship between AG and GD?

Back

AG is twice the length of GD. If AG = 16, then GD = 8.

Front

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

Back

AZ = 3 * 3 = 9.

Front

What is the formula to find the length of a segment from a vertex to the centroid?

Back

If the length from the vertex to the centroid is 'x', then the length from the centroid to the midpoint of the opposite side is 'x/2'.

Front

If AZ = 24, what is the length of AX if X is the centroid?

Back

AX = 24 / 1.5 = 16.

Front

What is the length of GE if BG = 10 and G is the centroid?

Back

GE = 10 / 2 = 5.

Front

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

Back

DG = 24 / 3 = 8.

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.

Front

How do you 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) for vertices (x1,y1), (x2,y2), (x3,y3).