Sect. 6.3 Medians and Centroids

Front

What is the centroid of 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 does the centroid divide each median in 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 G is the centroid and BE = 18, what is the length of BG?

Back

12

Front

If G is the centroid and GF = 4, what is the length of GC?

Back

8

Front

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

Back

21

Front

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

Back

The centroid divides the median into a ratio of 2:1, where the longer segment is twice the length of the shorter segment.

Front

If ZO = 24 and SZ = 3a - 9, how do you find the value of a?

Back

Set up the equation: 3a - 9 = 24, then solve for a to get a = 11.

Front

What is the formula for finding the length of a median in a triangle?

Back

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

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is significant because it is the balance point of the triangle and is used in various applications, including physics and engineering.

Front

How do you calculate the coordinates of the centroid of a triangle given its vertices?

Back

The coordinates of the centroid (G) can be calculated using the formula: G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3), where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.