Centroid

Front

What is the centroid of 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

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the relationship between the centroid and the medians?

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 a median is 12, what is the distance from the centroid to the vertex?

Back

The distance from the centroid to the vertex is 8, as the centroid divides the median in a 2:1 ratio.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

Can a segment be both a median and an altitude?

Back

Yes, in an isosceles triangle, the median from the vertex angle to the base is also an altitude.

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 = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the significance of the centroid in terms of balance?

Back

The centroid is the point at which a triangle can be balanced on the tip of a pencil, as it represents the center of mass.

Front

If the centroid divides a median in a 2:1 ratio, what is the length of the segment from the centroid to the midpoint if the entire median is 15?

Back

The length of the segment from the centroid to the midpoint is 5.