Question

What does orthocenter and centriod mean

Answer 1

The three altitudes intersect in a single point, called the orthocenter of the triangle. The orthocenter lies inside the triangle if and only if the triangle is acute (i.e. does not have an angle greater than or equal to a right angle). See also orthocentric system. If one angle is a right angle, the orthocenter coincides with the vertex of the right angle. Thus for acute and right triangles the feet of the altitudes all fall on the triangle.
The orthocenter, along with the centroid, circumcenter and center of the nine-point circle all lie on a single line, known as the Euler line. The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.
The isogonal conjugate and also the complement of the orthocenter is the circumcenter.
Four points in the plane such that one of them is the orthocenter of the triangle formed by the other three are called an orthocentric system or orthocentric quadrangle.

Answer 2

In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" (arithmetic mean) of all points of X. The definition extends to any object X in n-dimensional space: its centroid is the intersection of all hyperplanes that divide X into two parts of equal moment.
In physics, the word centroid means the geometric center of the object's shape, as above, but barycenter may also mean its physical center of mass or the center of gravity, depending on the context. Informally, the center of mass (and center of gravity in a uniform gravitational field) is the average of all points, weighted by the local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape.
In geography, the centroid of a region of the Earth's surface, projected radially onto said surface, is known as its geographical center.

Answer 3

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Answer 4

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