Question

What is a centroid?

a) The center of a circle passing through the vertices of a triangle
b) The point where the medians of a triangle intersect
c) The point where the perpendicular bisectors of a triangle intersect
d) The point where the altitudes of a triangle intersect

Answer 1

A centroid is the point where the medians of a triangle intersect and serves as the triangle's center of gravity. The correct answer is B.

Step-by-step explanation:

The student has asked about the definition of a centroid. The correct answer is b) The point where the medians of a triangle intersect. A centroid is a significant geometric concept and serves as the center of gravity within a triangle. This point is found by drawing the medians of a triangle, which are lines from each vertex to the midpoint of the opposing side. All three medians intersect at a single point, and this point is the centroid. It's important to note that the centroid is always inside the triangle and it divides each median into segments with a 2:1 ratio, the longer segment being adjacent to the vertex.

The centroid has various properties that are useful in different branches of mathematics and physics. For instance, in physics, the centroid is used to find the center of mass of a uniform solid triangle, as the entire mass of the triangle can be considered to be concentrated at this point for some calculations.

To summarize, 'centroid' should not be confused with concepts such as the center of a circle, the circumcenter (where perpendicular bisectors of a triangle intersect), or the orthocenter (where the altitudes of a triangle intersect).

Answer 2

b) The point where the medians of a triangle intersect

The centroid of a triangle is the point where the three medians of the triangle intersect. The median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.