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
The horizontal line is called the X – AXIS, and the vertical line is called
the Y – AXIS.
8. Parts of the Cartesian Plane
An ordered pair of the form (x, y) is the representation of a point on the
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).
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
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,
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
Point C: The coordinates of the point
are (2, 4).
Point D: The coordinates of the point
are (4, −4)