The rectangular coordinate system (also known as Cartesian plane) was developed by René Descartes and uses two perpendicular number lines (x-axis and y-axis) that intersect at the origin (0,0) to locate points in a plane. Any point is identified with an ordered pair (x,y) denoting its distances from the x-axis and y-axis. The axes divide the plane into four quadrants, and points can be plotted or identified from their coordinates.

1. RECTANGULAR COORDINATE SYSTEM

3. Rectangular Coordinate System
• French mathematician René Descartes (1596 – 1650) who is known as
the “Father of Modern Mathematics”, came up with this idea of his
coordinate system, the CARTESIAN PLANE.

4. Parts of the Cartesian Plane
It is composed of two perpendicular number lines that meet at the
point of ORIGIN (0, 0) and divide the plane into four regions called
QUADRANTS.
The horizontal line is called the X – AXIS, and the vertical line is called
the Y – AXIS.

5. Origin

6. Parts of the Cartesian Plane
QUADRANT X – COORDINATE Y - COORDINATE
I Positive Positive
II Negative Positive
III Negative Negative
IV Positive Negative

7. (+, -)
(-, +)
(-, -)
(+, +)

8. Parts of the Cartesian Plane
An ordered pair of the form (x, y) is the representation of a point on the
Cartesian plane.
The first coordinate of a point is called the x – coordinate or abscissa
and the second coordinate is called the y – coordinate or ordinate.

9. Plot (1, 3) and (3, 1).
Let’s begin with point (1, 3). The x-coordinate is 1 so find 1 on the x-
axis and sketch a vertical line through x = 1. The y-coordinate is 3 so
we find 3 on the y-axis and sketch a horizontal line through y = 3.
Where the two lines meet, we plot the point (1, 3).

10. Plot (1, 3) and (3, 1).
To plot the point (3, 1), we start by locating 3 on the x-axis and sketch a
vertical line through x = 3. Then we find 1 on the y-axis and sketch a
horizontal line through y = 1. Where the two lines meet, we plot the
point (3, 1).

11. Plot each point on the same rectangular coordinate system: (2, 5), (5, 2).

12. Plot each point in the rectangular coordinate system and identify the quadrant in
which the point is located:
a. (−1, 3)
b. (−3, −4)
c. (2, −3)
d. (3,
5
2
)

13. Plot each point:
a. (−5, 2)
b. (−5, −2)
c. (5, 2)
d. (5, −2)

14. Points on the Axes
• Points with a y-coordinate equal to 0 are on the x-axis, and have
coordinates (a, 0).
• Points with an x-coordinate equal to 0 are on the y-axis, and have
coordinates (0, b).
• What is the ordered pair of the point where the axes cross? At that
point both coordinates are zero, so its ordered pair is (0, 0). The point
has a special name. It is called the origin.
• The point (0, 0) is called the origin. It is the point where the x-axis and
y-axis intersect.

15. Plot each point on a coordinate grid:
a. (0, 5)
b. (4, 0)
c. (−3, 0)
d. (0, 0)
e. (0, −1)

16. Plot each point on a coordinate grid:
a. (−5, 0)
b. (3, 0)
c. (0, 0)
d. (0, −1)
e. (0, 4)

17. Identify Points on the Graph
• In algebra, being able to identify the coordinates of a point shown on
a graph is just as important as being able to plot points. To identify
the x-coordinate of a point on a graph, read the number on the x-axis
directly above or below the point. To identify the y-coordinate of a
point, read the number on the y-axis directly to the left or right of the
point. Remember, to write the ordered pair using the correct order (x,
y).

18. Name the ordered pair of each point shown:
Point A: The coordinates of the point
are (−3, 3).
Point B: The coordinates of the point are
(−1, −3).
Point C: The coordinates of the point
are (2, 4).
Point D: The coordinates of the point
are (4, −4)

19. Name the ordered pair of each point shown:

20. You try!
Illustrate a Cartesian plane. Plot and label the following points. Determine also
which quadrants the points lie.
1. C(0, 4)
2. A(3, -2)
3. R(-5, 3)
4. T(0, 7)
5. E(-3, -6)