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If the circles k and q are orthogonal, then a straight line passing through the center O of k and intersecting q, does so at inverse points with respect to k. Given a triangle OAB in which O is the center of a circle k, and points A' and B' inverses of A and B with respect to k, then
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
Step 1 (red): construct a circle with center at P and some fixed radius r to create points A′ and B′ on the line AB, which will be equidistant from P. Step 2 (green): construct circles centered at A′ and B′ having radius r. P and Q will be the points of intersection of these two circles. Point Q is then the reflection of point P through ...
Vertical – spanning the height of a body. Longitudinal – spanning the length of a body. Lateral – spanning the width of a body. The distinction between width and length may be unclear out of context. Adjacent – next to; Lineal – following along a given path. The shape of the path is not necessarily straight (compare to linear).
In mathematics, reflection through the origin refers to the point reflection of Euclidean space R n across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by − 1 {\displaystyle -1} , and can also be written as − I {\displaystyle -I} , where I ...
For example, the standard basis on R n provides a standard orientation on R n (in turn, the orientation of the standard basis depends on the orientation of the Cartesian coordinate system on which it is built). Any choice of a linear isomorphism between V and R n will then provide an orientation on V.
A vertical translation means composing the function + with f, for some constant b, resulting in a graph consisting of the points (, +) . Each point ( x , y ) {\displaystyle (x,y)} of the original graph corresponds to the point ( x , y + b ) {\displaystyle (x,y+b)} in the new graph, which pictorially results in a ...
Selecting reference points. In two dimensions, given an ordered set of three or more connected vertices (points) (such as in connect-the-dots) which forms a simple polygon, the orientation of the resulting polygon is directly related to the sign of the angle at any vertex of the convex hull of the polygon, for example, of the angle ABC in the picture.