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 do you find the centroid of a triangle given its vertices?

Back

To find the centroid (G) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3), use the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is a median in a triangle?

Back

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

Front

If a median divides a triangle into two smaller triangles, what can be said about their areas?

Back

The two smaller triangles have equal areas.

Front

In triangle ABC, if G is the centroid and AG = 4, what is the length of the entire median from A to the midpoint of BC?

Back

The entire median is 12, since the centroid divides each median in a 2:1 ratio.

Front

If the length of a median is 30, what is the distance from the centroid to the vertex?

Back

The distance from the centroid to the vertex is 20, as the centroid divides the median in a 2:1 ratio.

Front

What is the relationship between the lengths of segments created by the centroid on a median?

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 centroid G of triangle ABC is located at (2, 3), what is the sum of the coordinates of G?

Back

The sum of the coordinates of G is 5 (2 + 3).

Front

What type of segments are drawn from the vertices to the opposite sides in a triangle?

Back

Medians.

Front

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

Back

BE = 21, since the centroid divides the median in a 2:1 ratio.