Median and 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

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 lengths of the segments created by the centroid on a median?

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 a median is divided into segments of lengths 2x and x, what is the total length of the median?

Back

The total length of the median is 3x.

Front

If BE is a median and G is the centroid, what is the relationship between BE and BG?

Back

BG is two-thirds the length of BE.

Front

If the length of a median is 30, what is the length of the segment from the centroid to the midpoint of the opposite side?

Back

The length of the segment from the centroid to the midpoint is 10.

Front

What is the formula to find the length of a median in a triangle with vertices at coordinates (x1, y1), (x2, y2), (x3, y3)?

Back

The length of the median can be calculated using the formula: m = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a, b, and c are the lengths of the sides of the triangle.

Front

If the lengths of the sides of a triangle are 5, 12, and 13, what is the length of the median to the side of length 13?

Back

The length of the median to the side of length 13 is 6.

Front

What is the significance of the centroid in real-world applications?

Back

The centroid can be used in various fields such as engineering, architecture, and physics to determine the center of mass and balance of structures.