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Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where
Cardinal directions or cardinal points may sometimes be extended to include vertical position (elevation, altitude, depth): north and south, east and west, up and down; or mathematically the six directions of the x-, y-, and z-axes in three-dimensional Cartesian coordinates. Topographic maps include elevation, typically via contour lines.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. [10] This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the ...
The standard style for OpenStreetMap, like most Web maps, uses the Web Mercator projection. Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator [1] or WGS 84/Pseudo-Mercator is a variant of the Mercator map projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted ...
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
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Starting from the graph of f, a horizontal translation means composing f with a function , for some constant number a, resulting in a graph consisting of points (, ()) . Each point ( x , y ) {\displaystyle (x,y)} of the original graph corresponds to the point ( x + a , y ) {\displaystyle (x+a,y)} in the new graph ...
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