Centroids

Front

What is the definition of a centroid in a triangle?

Back

The centroid of a triangle is the point where the three medians intersect. It is also the center of mass of the triangle.

Front

How is the centroid related to the sides 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 ZX = 3, what is the length of AZ if X is the centroid?

Back

AZ = 9.

Front

If BX = 8, what is the length of BY if X is the centroid?

Back

BY = 12.

Front

If DL = 24, what is the length of DG?

Back

DG = 8.

Front

If G is the centroid of triangle ABC and BE = 18, what is the length of BG?

Back

BG = 12.

Front

If CW = 30, what is the length of CX if X is the centroid?

Back

CX = 20.

Front

What is the formula to find the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

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

Front

What is the significance of the centroid in geometry?

Back

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

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: Median = √(2a² + 2b² - c²) / 4, where a, b, and c are the lengths of the sides of the triangle.