Cartesian coordonate system : definition
From
Richard Hachel@21:1/5 to
All on Thu May 8 18:32:02 2025
A Cartesian coordinate system is a coordinate system used to locate points
in space using perpendicular lines called axes.
In a (2D) plane, a Cartesian coordinate system is generally composed of:
Two axes: the horizontal axis (called the x-axis), denoted by π₯, and
the vertical axis (called the y-axis), denoted by π¦.
An origin point, denoted by π, where the two axes intersect.
Identical units of measurement on each axis to allow for regular reference points.
Each point on the plane can be represented by a pair of numbers
(π₯,π¦), called Cartesian coordinates.
These numbers indicate the position on the π₯-axis and the π¦-axis, respectively.
A wide variety of mathematical elements can be plotted in a Cartesian
plane, including:
- Points. Each point is defined by its coordinates (x,y).
- Line segments and lines. A line segment connects two points. A line can
be drawn from an equation like y=2x+1.
- Curves (parabolas, circles, ellipses, hyperbolas, exponential functions, sinusoidal functions, etc.).
When a line (such as a curve representing a function) crosses the x-axis
in a Cartesian coordinate system, this point of intersection is called:
- a zero of the function
- a root of the function
- or a solution to the equation f(x)=0
These three terms are synonymous in this context.
Example: for the function f(x) = e^x - 1, we are looking for the value for which f(x)=0.
Now, the curve f(x) intersects the x-axis at x=0. We say that x=0 is a
root (or zero) of the function.
R.H.
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