The document describes the Cartesian coordinate system, which uses perpendicular x and y axes that intersect at the origin (0,0) to locate and plot points on a plane. The x-axis divides the plane into positive and negative numbers, and likewise for the y-axis, creating four quadrants. Ordered pairs (x,y) are used to specify points, with the x-value being the abscissa and y-value being the ordinate.

1. THE CARTESIAN
COORDINATE SYSTEM
Mathematics 8

2. A Cartesian plane is a graph with
one x-axis and one y-axis (that’s
why it’s sometimes called an X Y
graph). These two axes are
perpendicular to each other.
The origin (O) is in the exact
center of the graph. Numbers to
the right of the zero on the x-
axis are positive; numbers to the
left of zero are negative. For the
y-axis, numbers below zero are
negative and numbers above are
positive.
What is Cartesian
Coordinate
System/Cartesian Plane?

3. ● First Quadrant = Top right.
● Second Quadrant = Top left.
● Third Quadrant = Bottom left.
● Fourth Quadrant = Bottom right.
Fun fact: The invention of this
system was revolutionary for its
time. It gave us the first
systematic link between algebra and
geometry.
Cartesian Plane
Quadrants

4. ● Ordinate and abscissa refer
to ordered pairs on a
Cartesian plane.
● The abscissa is the x-
value (the first number
in an ordered pair).
● The ordinate is the y-
value (the second number
in an ordered pair).
Ordinate and Abscissa
on a Cartesian Plane

5. What is an Origin?
It is often denoted by O, and the coordinates are always zero. In one
dimension we simply write the origin as 0; it’s the point where we
start numbering on a number line. You can go in either of two
directions:
● Going left, you would count off negative numbers
● Going right, you would count off with positive numbers.
Either way you can go an infinite distance (to infinity or negative
infinity).
A number line showing the distance between -1 and 1. 0 is in the center.

6. In two dimensions, using the
Cartesian plane, an origin is the
point where the x and y axes
intersect. This point is written
as (0, 0).
Origin on a
Cartesian Plane

7. Practice Problem
Locate below points on the Cartesian
Coordinate System. Also, mention the
quadrant points belong to.
(i) (2, 3)
(ii) (-3, 1)
(iii) (-1.5, -2.5)
(iv) (0,0)

9. Performance Task
You are both architects and engineers, and you work
for the Engineering Department of your local
municipality. Your department head has charged you
with the responsibility of delivering to the barangay
captains in your town a three-dimensional miniature
model of a business that is doing very well
commercially.
Be guided to the location of the establishments:
1. School (1,3); Quadrant 1
2. Milktea Shop (5,-4); Quadrant 4
3. Shopping Mall (-4,-2); Quadrant 3
4. Amusement Part (-3,4); Quadrant 2
5. Clinic (0, -10); y-axis