Cartesian Coordinate System.pdf

THE CARTESIAN
COORDINATE SYSTEM
Mathematics 8
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?
● 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
● 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
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.
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
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)
Cartesian Coordinate System.pdf
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
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Cartesian Coordinate System.pdf

  • 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