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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.
In common usage, the abscissa refers to the x coordinate and the ordinate refers to the y coordinate of a standard two-dimensional graph. [1] [2]The distance of a point from the y axis, scaled with the x axis, is called the abscissa or x coordinate of the point.
When viewed at a position along the positive z-axis, the ¼ turn from the positive x-to the positive y-axis is counter-clockwise. For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise. Interchanging the labels of any two axes reverses the handedness.
For an xyz-Cartesian coordinate system in three dimensions, suppose that a second Cartesian coordinate system is introduced, with axes x', y' and z' so located that the x' axis is parallel to the x axis and h units from it, the y' axis is parallel to the y axis and k units from it, and the z' axis is parallel to the z axis and l units from it.
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.
One does not need to construct the convex hull of a polygon to find a suitable vertex. A common choice is the vertex of the polygon with the smallest X-coordinate. If there are several of them, the one with the smallest Y-coordinate is picked. It is guaranteed to be a vertex of the convex hull of the polygon.
To be able to plot points, one needs to first decide on a point in plane which will be called the origin, and a couple of perpendicular lines, called the x and y axes, as well as a preferred direction on each of the lines. Usually one chooses the x axis pointing right and the y axis pointing up, and these will be named the positive directions ...
The four quadrants of a Cartesian coordinate system. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.