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For any point, the abscissa is the first value (x coordinate), and the ordinate is the second value (y coordinate). In mathematics , the abscissa ( / æ b ˈ s ɪ s . ə / ; plural abscissae or abscissas ) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system : [ 1 ] [ 2 ]
The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- and the y-axis form a positively oriented two-dimensional coordinate system in the xy-plane if observed from above the xy-plane) is called right-handed or positive. 3D Cartesian coordinate handedness. The name derives from the right-hand rule.
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.
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the
If (x 0, y 0) is such a critical point, then x 0 is the corresponding critical value. Such a critical point is also called a bifurcation point, as, generally, when x varies, there are two branches of the curve on a side of x 0 and zero on the other side.
Points can then be located with reference to the origin by giving their numerical coordinates—that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three.
Graph = with the -axis as the horizontal axis and the -axis as the vertical axis.The -intercept of () is indicated by the red dot at (=, =).. In analytic geometry, using the common convention that the horizontal axis represents a variable and the vertical axis represents a variable , a -intercept or vertical intercept is a point where the graph of a function or relation intersects the -axis of ...
On the other hand, the completions with respect to the other non-trivial absolute values give the fields of p-adic numbers, where is a prime integer number (see below); since the -adic absolute values satisfy the ultrametric property, then the -adic number fields are non-Archimedean as normed fields (they cannot be made into ordered fields).