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 shorter segment being one third the length of the entire median.

Front

If AG is 16 and G is the centroid, what is the length of GD?

Back

8 (GD is one third of AG).

Front

If BF is 10, what is the length of AF if CF, BE, and AD are medians?

Back

10 (AF is equal to BF in this case).

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex of the triangle to the midpoint of the opposite side.

Front

What is the relationship between the centroid and the area of a triangle?

Back

The centroid divides the triangle into three smaller triangles of equal area.

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 significance of the centroid in physics?

Back

The centroid represents the center of mass of a triangular object, which is important for balance and stability.

Front

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

Back

16 (AX is two thirds of AZ).

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.