Coordinate axes

(noun)

A set of perpendicular lines which define coordinates relative to an origin. Example: x and y coordinate axes define horizontal and vertical position.

Related Terms

Examples of Coordinate axes in the following topics:

  • Adding and Subtracting Vectors Graphically

    • Vectors may be added or subtracted graphically by laying them end to end on a set of axes.
    • The head-to-tail method of vector addition requires that you lay out the first vector along a set of coordinate axes.
    • To start, draw a set of coordinate axes.
    • Next, draw out the first vector with its tail (base) at the origin of the coordinate axes.
    • The head-to-tail method of vector addition requires that you lay out the first vector along a set of coordinate axes.

  • Scalars vs. Vectors

    • The two parts are its length which represents the magnitude and its direction with respect to some set of coordinate axes.
    • Typically this reference point is a set of coordinate axes like the x-y plane.

  • The Cartesian System

    • The Cartesian coordinate system is used to specify points on a graph by showing their absolute distances from two axes.
    • The point where the axes intersect is known as the origin.
    • A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to the two axes.
    • The origin where the two axes meet is thus $(0,0)$.  
    • The Cartesian coordinate system is broken into four quadrants by the two axes; labeled, I, II, III, and IV, starting from the upper right and continuing counter-clockwise as pictured below.

  • Regional Terms and Axes

    • The X, Y, and Z axes of the Cartesian coordinate system are used describe the specific location of an axis in standard anatomical position.
    • Many types of axes can give regional direction.
    • It is perpendicular to both the DV and AP axes.
    • Describe how axes give direction, detail, and location when describing a region of the body

  • Defining Trigonometric Functions on the Unit Circle

    • The x- and y-axes divide the coordinate plane (and the unit circle, since it is centered at the origin) into four quarters called quadrants.
    • The diagram below illustrates these coordinates.
    • We know that, for any point on a unit circle, the $x$-coordinate is $\cos t$ and the $y$-coordinate is $\sin t$.
    • We can find the coordinates of any point on the unit circle.
    • The unit circle, showing coordinates and angle measures of certain points.

  • Parts of a Hyperbola

    • We will use the x-axis hyperbola to demonstrate how to determine the features of a hyperbola, so that $a$ is associated with x-coordinates and $b$ is associated with y-coordinates.
    • The vertices have coordinates $(h + a,k)$ and $(h-a,k)$.
    • The major and minor axes $a$ and $b$, as the vertices and co-vertices, determine a rectangle that shares the same center as the hyperbola and has dimensions $2a \times 2b$.
    • The foci have coordinates $(h+c, k)$ and $(h-c,k)$.
    • The asymptotes of a rectangular hyperbola are the x- and y-axes.

  • Components of a Vector

    • Vectors are geometric representations of magnitude and direction which are often represented by straight arrows, starting at one point on a coordinate axis and ending at a different point.
    • A vector is defined by its magnitude and its orientation with respect to a set of coordinates.
    • To visualize the process of decomposing a vector into its components, begin by drawing the vector from the origin of a set of coordinates.
    • The original vector, defined relative to a set of axes.
    • The horizontal component stretches from the start of the vector to its furthest x-coordinate.

  • Three-Dimensional Coordinate Systems

    • The three-dimensional coordinate system expresses a point in space with three parameters, often length, width and depth ($x$, $y$, and $z$).
    • Each parameter is labeled relative to its axis with a quantitative representation of its distance from its plane of reference, which is determined by the other two parameter axes.
    • This is a three dimensional space represented by a Cartesian coordinate system.
    • The cylindrical coordinate system is like a mix between the spherical and Cartesian system, incorporating linear and radial parameters.
    • Identify the number of parameters necessary to express a point in the three-dimensional coordinate system

  • Vectors in Three Dimensions

    • The mathematical representation of a physical vector depends on the coordinate system used to describe it.
    • In the Cartesian coordinate system, a vector can be represented by identifying the coordinates of its initial and terminal point.
    • Typically in Cartesian coordinates, one considers primarily bound vectors.
    • A bound vector is determined by the coordinates of the terminal point, its initial point always having the coordinates of the origin $O = (0,0,0)$.
    • $\mathbf{i}$, $\mathbf{j}$, and $\mathbf{k}$ are unit vectors along the $x$-, $y$-, and $z$-axes, respectively.

  • What is a Quadratic Function?

    • Quadratic equations are second order polynomials, and have the form $f(x)=ax^2+bx+c$.
    • where $h$ and $k$ are respectively the coordinates of the vertex, the point at which the function reaches either its maximum (if $a$ is negative) or minimum (if $a$ is positive).