Geometry Practice: Section 5.3Finding Centroids and Orthocenters

Front

What is the centroid of a triangle?

Back

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

Front

How do you find the centroid of a triangle with vertices at (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (C) can be found using the formula: C = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of the triangle intersect.

Front

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, you need to determine the equations of the altitudes and find their intersection point.

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

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

What is the relationship between the centroid and the orthocenter in a triangle?

Back

The centroid, orthocenter, circumcenter, and incenter are all points of concurrency in a triangle, but they have different properties and locations.

Front

How do you calculate the length of a segment given two endpoints (x1, y1) and (x2, y2)?

Back

The length of the segment can be calculated using the distance formula: length = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.