# Direction of x-axis with respect to y-axis in Cartesian coordinate system?

What should be the direction of y-axis with respect to x-axis in cartesian coordinate system ?

It should be on right hand side or left hand side of x-axis or it can be on both sides as long as it is perpendicular to x-axis ?

Plus

Angles in counterclockwise rotation are considered positive when they are measured from positive x-axis. What if the rotation is clockwise ? From which axis the angles will be considered positive if the rotation is clockwise ?

• Our universe is a left handed one, so you rotate 90 degrees anti-clockwise to get the y axis. – Sonal_sqrt Feb 19 '18 at 7:19
• great @PiyushDivyanakar. ans what about angles if the rotation is clockwise? – Alex Feb 19 '18 at 7:23
• if angles go anti-clockwise it is the left handed system. If they clockwise it is the right handed system. The rule is the same, you rotate 90 degrees(depending on handedness). – Sonal_sqrt Feb 19 '18 at 7:25
• look at this link please they take y axis at clock wise rotation with respect to x-axis. are they wrong ?. en.wikibooks.org/wiki/Geometry_for_Elementary_School/… – Alex Feb 19 '18 at 7:28
• It is correct. It is a matter of convention. – Sonal_sqrt Feb 19 '18 at 7:31

It is solely matter of convention, in one case we talk of Right Hand System in the second of Left Hand System, note indeed that we need also to fix a z axes direction to define a clockwise and a counterclockwise direction for rotation.  • please expain in two dimensions. only x-y. kindly tell me is there a rule that tells us when to use right hand coordinates and when to use left hand coordinates while applying them ? – Alex Feb 19 '18 at 7:34
• @Alex In 2 dimension all system are equivalent since you cannot distinguish them, fixed x, say on the right, we can choose y up or down and those are equivalent choices. Otherwise in 3 dimension we can have 2 kinds of reference systems and we have to declare which one we are referring to. – gimusi Feb 19 '18 at 7:38
• suppose a system is rotating ?then will we take y-axis on counter clockwise direction if the body is rotating counter clockwise. and we will take y in clockwise direction if the body is rotating clockwise? – Alex Feb 19 '18 at 8:22
• To define a clockwise direction we need to fix a direction for the z axes, otherwise we can’t distinguish one system from another. The usual convention is consider a RHS with z axes up out of the plane, with x axes direction on the right, in this case y axes direction is up. – gimusi Feb 19 '18 at 8:28

The $x$-axis (also known as the abscissa) goes horizontally and the $y$-axis (also known as the ordinate) goes vertically. This is because, \begin{align} x &= \text{ the independent variable; and} \\ y &= \text{ the dependent variable.}\end{align} This means that from these, we can measure data (typically for scientific purposes) and graph equations. When conducting a science experiment, we look at cause and effect, and how $$\text{Cause}\longrightarrow\text{Effect}.$$ Here, there are two variables in our experiment. The variable that creates the cause, namely $x$, and the variable that becomes the effect of that cause, namely $y$. $$\underbrace{\text{Cause}}_{x} \longrightarrow\underbrace{\text{Effect}}_{y}.$$ It follows, then, that the variable $y$ depends on that of $x$, and so is dependent, with $x$ being vice versa (namely independent).

There are other elements under investigation during a scientific experiment, but this is where the graph originated from, and we just applied it mathematically by writing out an equation to describe the relationship between the cause and effect (the $x$ variable to the $y$ variable). For different forms of equations, we have different relationships. For example, the equation $$y = mx + c$$ describes the linear relationship between $x$ and $y$. And the equation, $$y = ax^2 + bx + c$$ describes the quadratic relationship between $x$ and $y$. We graph these equations from plotting points on our graph, for which their position on the graph corresponds to an $x$ point and a $y$ point. We represent this as a coordinate $(x, y)$. Notice that this word derives from the word ordinate which is the $y$-axis. However, when we have a coordinate $(x, y)$ that is not plotted on the graph, this is known as an ordered pair. This is necessary because we can write equations like, \text{Find (x, y) over the integers if y^2 = 2x^2 - 1}.\tag*{\bigg(\begin{align} &\text{This is a negative Pell} \\ &\text{equation by the way.}\end{align}\bigg)} Now we also have a third axis, namely the $z$-axis, to form ordered triplets $(x, y, z)$. This is the final axis, for the Cartesian Plane measures our dimensions only in space, namely $3$, and that’s where equations can get a bit more interesting, but when measuring scientific data, we stick with $x$ and $y$.

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