![math illustrations planes math illustrations planes](https://cdn.w600.comps.canstockphoto.com/more-less-equal-with-cartoon-illustration_csp90044422.jpg)
![math illustrations planes math illustrations planes](https://i5.walmartimages.com/asr/3bce9bfc-0eb9-4f69-828a-8f51ca6e3f35_1.dd6f6faaaf5a06506bbc3e52c6bc5251.jpeg)
Lastly, the $yz$-plane is the vertical plane spanned by the $y$ and the $z$-axis and contains the right wall in the room analogy. Similarly, the $xz$-plane is the vertical plane spanned by the $x$ and $z$-axes and contains the left wall in the room analogy. It is identical to the two-dimensional coordinate plane and contains the floor in the room analogy. The $xy$-plane is the horizontal plane spanned by the $x$ and $y$-axes. In addition to the three coordinate axes, we often refer to three coordinate planes. Since these pages are written in the right-handed universe, we suggest you live in our universe while studying from these pages. The problem is that switching universes will change the sign on some formulas. The right-handed and left-handed coordinate systems represent two equally valid mathematical universes. Switching the locations of the positive $x$-axis and positive $y$-axis creates left-handed coordinate system. With above definitions of the positive $x$, $y$, and $z$-axis, the resulting coordinate system is called right-handed if you curl the fingers of your right hand from the positive $x$-axis to the positive $y$-axis, the thumb of your right hand points in the direction of the positive $z$-axis. You can drag the figure with the mouse to rotate it. The branch of each axis on the opposite side of the origin (the unlabeled side) is the negative part. The origin is the intersection of all the axes. The positive $x$-axis, positive $y$-axis, and positive $z$-axis are the sides labeled by $x$, $y$ and $z$. A representation of the three axes of the three-dimensional Cartesian coordinate system. Three-dimensional Cartesian coordinate axes. The negative part of these axes would be the continuations of the lines outside of the room, illustrated by the unlabeled halves of each axis, below. 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.
![math illustrations planes math illustrations planes](https://ourjourneywestward.com/wp-content/uploads/2012/10/paper-airplane-math.jpg)
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.
![math illustrations planes math illustrations planes](https://cdn.shopify.com/s/files/1/1202/7532/products/92-94_chevy_blazer_to_06_conversion_fenders_1024x1024.jpg)
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.