The document describes the rectangular coordinate system, highlighting the role of the x-axis and y-axis in defining a flat surface known as a plane, where each point is represented by an ordered pair (x,y). It outlines the characteristics and position of the quadrants in the Cartesian plane and provides instructions for plotting points and identifying figures based on specified coordinates. Additionally, it includes a historical note on René Descartes, the system's namesake, and a practical application involving plotting various coordinate pairs.

1. Rectangular
Coordinate
System

2. H
G GRADE 12
F GRADE 11 CANTEEN WORKSHOP GARDEN
E GRADE 10
D FLAGPOLE GRADE 9
C GUARD HOUSE GRADE 8
B PRINCIPAL’S OFFICE
A GRADE 7
1 2 3 4
1. CANTEEN
2. GRADE 8
3. GRADE 7
4. WORKSHOP
5. GUARD HOUSE
= 2F
= 4C
= 3A
= 3F
= 1C
FIND THE COORDINATES

3. CARTESIAN
COORDINATE
PLANE

4. • The rectangular coordinate system consists of two real number lines
that intersect at a right angle.
• The horizontal number line is called the x-axis, and the vertical
number line is called the y-axis.
• These two number lines define a flat surface called a plane, and each
point on this plane is associated with an ordered pair of real
numbers(x,y).
• The first number is called the x-coordinate or the abscissa of the
point, and the second number is called the y-coordinate or the
ordinate of the point.
• The intersection of the two axes is known as the origin, which
corresponds to the point (0, 0).
• The x-axis is often called the axis of abscissa and the y-axis is called
as axis of coordinate.

5. • The coordinate system we commonly use is called the Cartesian system, after the
French mathematician René Descartes (1596-1650), who developed it in the 17th
century. Legend has it that Descartes, who liked to stay in bed until late, was
watching a fly on the ceiling from his bed. He wondered how to best describe the
fly's location and decided that one of the corners of the ceiling could be used as a
reference point.
René Descartes also known as the Father of
Modern Mathematics

6. • In quadrant I, both the axis are positive. (+ , +)
• In quadrant II, x-axis is negative and y-axis is positive. (- , +)
• In quadrant III, both axis are negative. (- , -)
• In quadrant IV, x-axis is positive and y-axis is negative. (+ , -)
QUADRANTS

7. 1. (-3, 4)
2. (-1, 1)
3. (2, -7)
4. (5, 6)
5. (-3, -2)
= QUADRANT II
= QUADRANT II
= QUADRANT IV
= QUADRANT I
= QUADRANT III
IDENTIFY THE QUADRANTS
6. (1, 4)
7. (2, 0)
8. (0, -8)
9. (1, 6)
10. (-8, -13)
= QUADRANT I
= NOT IN ANY QUADRANT
= NOT IN ANY QUADRANT
= QUADRANT I
= QUADRANT III

8. PLOTTING THE COORDINATES
Plot these pairs
1 2 3 4 5 6 7
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
8
7
-8
8
-1
-2
-3
-4
-5
-6
-7
y
x
(3,7)
1. (3,7)
2. (-4,3)
(-4,3)
3. (-3,-2)
(-3,-2)
4. (4,-6)
(4,-6)
5. (5,-2)
(5,-2)

9. PLOTTING THE COORDINATES
Plot these pairs. (-3,7), (-4,-1), (7,-3) and connect
1 2 3 4 5 6 7
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
8
7
-8
8
-1
-2
-3
-4
-5
-6
-7
y
x
(-3,7)
(-4,-1)
(7,-3)

10. PLOTTING THE COORDINATES
Plot these pairs. (3,3), (-3,3), (-3,-3),(3,-3) and connect
1 2 3 4 5 6 7
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
8
7
-8
8
-1
-2
-3
-4
-5
-6
-7
y
x
(3,3)
(-3,3)
(-3,-3) (3,-3)

11. PLOTTING THE COORDINATES
Plot these pairs. (3,3), (3,-3), (-3,-3),(3,-3) and connect
1 2 3 4 5 6 7
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
8
7
-8
8
-1
-2
-3
-4
-5
-6
-7
y
x
(3,3)
(-3,3)
(-3,-3) (3,-3)

12. WORLD MAP COORDINATES

13. MAP COORDINATES

14. MAP COORDINATES

15. Draw a Cartesian plane and plot the following points. Then
connect all the points according to the sequence of letters
indicated below and identify the figure formed.
1. (0, 4)
2. (-3, -4)
3. (4, 1)
4. (-4, 1)
5. (3, -4)