3. Rectangular Coordinates
A good way of presenting a function is by graphical representation.
Graphs give us a visual picture of the function.
The most common way to graph a function is to use the rectangular co-ordinate system. This consists of:
The origin `(0,0)`; and
The four quadrants, normally labelled I, II, III, IV.
The cartesian plane
Where did all this come from?
The x-y coordinate system is also called the Cartesian Coordinate system, after its developer, Rene Descartes (1596 - 1650). This graphing system was incredibly important for the advancement of science and engineering.
Normally, the values of the independent variable (generally the x-values) are placed on the horizontal axis, while the values of the dependent variable (generally the y-values) are placed on the vertical axis.
The x-value, called the abscissa, is the perpendicular distance of P from the y-axis.
The y-value, called the ordinate, is the perpendicular distance of P from the x-axis.
The values of x and y together, written as (x, y) are called the co-ordinates of the point P.
It's called the "rectangular" coordinate system because the scale used along the x-axis is evenly spaced, as is the scale along the y-axis. Other systems exist where the scale is not even (see Log-log and semi-log graphs) and some are even circular (see Polar Coordinates)
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Need Graph Paper?
Locate the points `A(2 , 1)` and `B(-4 , -3)` on the rectangular co-ordinate system.
Three vertices of a rectangle are `A(-3 , -2)`, `B(4 , -2)` and `C(4,1)`.
Where is the fourth vertex `D`?
Where are all points `(x , y)` for which `x < 0` and `y < 0`?
Q1 Where are all the points whose abscissas equal their ordinates?
Q2 Where are all the points `(x, y)` for which `x = 0` and `y < 0`?