The parts of the lines that you see while standing in the room are the positive portion of each of the axes, illustrated by the halves of the each axis labeled by $x$, $y$, and $z$ in the below applet. The $z$-axis is the vertical line along which the walls intersect. The $y$-axis is the horizontal line along which the wall to your right and the floor intersect. The $x$-axis is the horizontal line along which the wall to your left and the floor intersect. You can imagine the origin being the point where the walls in the corner of a room meet the floor. The three axes intersect at the point called the origin.
In three-dimensional space, the Cartesian coordinate system is based on three mutually perpendicular coordinate axes: the $x$-axis, the $y$-axis, and the $z$-axis, illustrated below. Cartesian coordinates of three-dimensional space You can change the location of the point by dragging it with your mouse. The Cartesian coordinates $(x,y)$ of the blue point specify its location relative to the origin, which is the intersection of the $x$- and $y$-axis. It's similar to the above figure, only it allows you to change the point.Ĭartesian coordinates in the plane. The below applet illustrates the Cartesian coordinates of a point in the plane. The following figure, the point has coordinates $(-3,2)$, as the point is three units to the left and two units up from the origin. Similarly, the second number $y$ is called the $y$-coordinate (or $y$-component), as it is the signed distance from the origin in the direction along the $y$-axis, The $y$-coordinate specifies the distance above (if $y$ is positive) or below (if $y$ is negative) the $x$-axis. The $x$-coordinate specifies the distance to the right (if $x$ is positive) or to the left (if $x$ is negative) of the $y$-axis. The first number $x$ is called the $x$-coordinate (or $x$-component), as it is the signed distance from the origin in the direction along the $x$-axis. The Cartesian coordinates of a point in the plane are written as $(x,y)$. The origin is the intersection of the $x$ and $y$-axes. The Cartesian coordinates in the plane are specified in terms of the $x$ coordinates axis and the $y$-coordinate axis, as illustrated in the below figure. The Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two-dimensions) or a triplet of numbers (in three-dimensions) that specified signed distances from the coordinate axis. Cartesian coordinates allow one to specify the location of a point in the plane, or in three-dimensional space.
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