Cartesian Plane
What is the Cartesian Plane?
A french Mathematician named Rene Descartes formalised its use in mathematics.
It is a 2-Dimensional plane that is used to visualize coordinates of a given relationship e.g. y=2x.
It is like two number lines crossing each other at zero, with one line being vertical and other horizontal.It is used to display all sorts of functions such as linear lines, circles, parabolas, etc. It is called 2-Dimensional because the relationship between only 2 variables can be displayed.
Components of Cartesian Plane
• It consists of two perpendicular lines:
i) Vertical line = y-axis = (line representing the y values)
ii) Horizontal line = x-axis = (line representing the x values)
These two combined represent the ordered pair from table of values (TOV) which are written in the form (x,y) e.g. in an ordered pair (6,7); the coordinate 6 represents a point on the x-axis, while 7 represents the point on y-axis.
Moreover, the lines cover both positive and negative sides so as to include all integer values when plotting a relationship. In the case of the x-axis, the left side represents the negative side and the right represents the positive (hint: right things are good so positive). As for the y-axis, the upper side is positive while the lower is negative.
• The point where both x and y axes intersect is referred to as origin and is represented by the ordered pair (0,0).
This all is displayed in the figure below.
Examples of Cartesian Plane
Plot the following ordered pairs on the graph.
i) (0,0)
Explanation
As mentioned earlier 0,0 is the origin so it is going to be at the point where the two axes intersect.
ii) (-3,2)
Explanation
In this case, x is negative so we move left 3 blocks from the origin and for the y value, 2 up because it is positive.
iii) (-3,-4)
Explanation
In this case both the values are negative so we move left 3 and down 4 from the origin.
Practice problems for Cartesian Plane
It's your turn to give it a try now.
Plot the following on a Cartesian Plane
1. (1, 5)
2. (-2,-4)
3. (3, 3)
4. (6,-5)
5. (-7,-2)
Take Home Points for Cartesian Plane
• It is common to mix-up the order of variables in the ordered pair x or y, what comes first? (hint: follow alphabetic order, x comes before y) therefore ordered pair = (x,y). x always comes before y.
• Moreover, watch out for the signs, and make sure you place the point accordingly i.e. negative on negative side and positive on positive. Remember, origin is your reference point. The positive side is right and at the top, and the negative side is left and at the bottom.
• Another thing to consider is the scaling of the plane. Make sure your scale is consistent throughout i.e. 1 block = 1 unit. There can be situations where you would have to change the scale to fit your data better, in that case, you should mention the scale of your choice in a legend and then stay consistent on either side of the axis. E.g. If you choose that 1 block = 2 units for the x-axis, it should be the same for both positive and negative sides for a given axis.
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