Cartesian coordinate system

A Cartesian coordinate system, also known as rectangular coordinate system, can be used to plot points and graph lines. The following is an example of rectangular coordinate system

Coordinate system


It is basically, a set of two number lines

The horizontal line is called x-axis and the vertical line is called y-axis

A good real life example of a vertical number line or y-axis is a thermometer.

Notice that it has 4 quadrants.

In quadrant I, x and y are positive

In quadrant II, x is negative, but y is positive

In quadrant III, x and y are negative

In quadrant IV, x is positive, but y is negative

The center, or intersection of the two axis is equal to (0,0)

In this lesson, you will learn to plot points on the cartesian coordinate system.

A point is represented by a pair of numbers (x, y)

x stands for any value on the x-axis and y stands for any value on the y-axis

An example of a point is (1, 5)

Let us now plot some points.

Locate point (2,3).

x = 2 and y = 3

Draw a vertical line at x = 2 and draw a horizontal line at y = 3

Where the two lines meet or intersect, is your point (in red)

(2, 3) on the coordinate system


Locate point (-3, 1)

Draw a vertical line at x = -3 and draw a horizontal line at y = 1

The intersection of the two lines is your point

(-3, 1) on the coordinate system


Locate point (-4, -4)

Draw a vertical line at x = -4 and draw a horizontal line at y = -4

(-4, -4) on the coordinate system


Tricky cases are when points are located on the x-axis or the y-axis.

Students usually get confused, so study the following two examples carefully

Locate point (2,0)

Draw a vertical line at x = 2 and draw a horizontal line at y = 0.

Notice that when y = 0, your horizontal line is on the x-axis

Important point to remember:

When y = 0, your point is always located on the x-axis

(2, 0) on the coordinate system


Locate point (0, -3)

Draw a vertical line at x = 0 and draw a horizontal line at y = -3.

Notice that when x = 0, your vertical line is on the x-axis

Important point to remember:

When x = 0, your point is always located on the y-axis

(0, -3) on the coordinate system
Other examples:

Points on the cartesian coordinate system

Take the quiz below about Cartesian coordinate system

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