Centroid

Front

What is the definition of a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and 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 G is the centroid of triangle ABC, and AG = 16, what is the length of GD?

Back

8 (Since the centroid divides the median in a 2:1 ratio, GD = AG/2).

Front

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

Back

8 (GC = 2 * GF, since G divides the median in a 2:1 ratio).

Front

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

Back

16 (AX = AZ/1.5, since the centroid divides the median in a 2:1 ratio).

Front

What is the ratio in which the centroid divides the median of a triangle?

Back

The centroid divides the median in a 2:1 ratio, with the longer segment being closer to the vertex.

Front

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

Back

21 (BE = 3 * GE, since G divides the median in a 2:1 ratio).

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is the balance point of the triangle and is used in various applications, including physics and engineering.

Front

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

Back

9 (AZ = 3 * 3, since the centroid divides the median in a 2:1 ratio).

Front

What is the formula to 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) where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.