This document defines and explains coordinate geometry. It begins by defining a grid, coordinate grid, x-axis, and y-axis. It then discusses plotting and finding ordered pairs on a coordinate grid with four quadrants by following steps of first locating the x-value and then the y-value, and whether numbers are positive or negative determines the direction. Examples are provided to demonstrate plotting various ordered pairs in all four quadrants of the coordinate system.

1. Coordinate Geometry
by Monica Yuskaitis

2. Definition
 Grid – A pattern of horizontal and
vertical lines, usually forming
squares.
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3. Definition
 Coordinate grid – a grid used to
locate a point by its distances from
2 intersecting straight lines.
A
B
C
D
E
What are the
coordinates
for the house?
1 2 3 4 5
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4. Definition
 x axis – a horizontal number line
on a coordinate grid.
0 1 2 3 4 5 6
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x

5. Hint
 x is the shortest and likes to lie
down horizontally.
0 1 2 3 4 5 6
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x

6. Definition
 y axis – a vertical number line on
a coordinate grid.
y
6
5
4
3
2
1
0
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7. Hint
 y is the tallest and stands upright or
vertically.
y
6
5
4
3
2
1
0
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8. Definition
 Coordinates – an ordered pair of
numbers that give the location of a
point on a grid. (3, 4)
6
5
(3,4)
4
3
2
1
00 1 2 3 4 5 6
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9. Hint

The first number is always the x or first letter
in the alphabet. The second number is always
the y the second letter in the alphabet.
6
5
(3,4)
4
3
2
1
00 1 2 3 4 5 6
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10. How to Plot Ordered Pairs
 Step 1 – Always find the x value
first, moving horizontally either right
(positive) or left (negative). (2, 3)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

11. 
How to Plot Ordered Pairs
Step 2 – Starting from your new position
find the y value by moving vertically
either up (positive) or down (negative).
6
(2, 3) 5
4
(2,3)
y 3
2
1
00 1 2 3 4 5 6 x
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12. 
How to Find Ordered Pairs
Step 1 – Find how far over horizontally
the point is by counting to the right
(positive) or the left (negative). (5, )
6
5
4
y 3
2
1
00 1 2 3 4 5 6 x
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13. How to Find Ordered Pairs
 Step 2 – Now count how far
vertically the point is by counting up
(positive) or down (negative).
(5,4)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

14. What is the ordered pair?
(3,5)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

15. What is the ordered pair?
(2,6)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

16. What is the ordered pair?
(4,0)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

17. What is the ordered pair?
(0,5)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

18. What is the ordered pair?
(1,1)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
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x

19. Four Quadrants of Coordinate Grid
 When the number lines are extended into
the negative number lines you add 3 more
quadrants to the coordinate grid.
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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20. Four Quadrants of Coordinate Grid
 If the x is negative you move to
the left of the 0. x = -2
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
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x

21. Four Quadrants of Coordinate Grid
 If the y is negative you move
down below the zero. y = -3
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
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x

22. How to Plot in 4 Quadrants
 Step 1 - Plot the x number first
moving to the left when the
number is negative. (-3, -2)
3
y
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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23. How to Plot in 4 Quadrants
 Step 2 - Plot the y number
moving from your new position
down 2 when the number is
y
negative.3
2
(-3, -2) 1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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24. How to Plot in 4 Quadrants
 When x is positive and y is
negative, plot the ordered pair in
this manner.
y
3
2
(2, -2) 1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
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x

25. How to Plot in 4 Quadrants
 When x is negative and y is
positive, plot the ordered pair in
this manner.
y
3
2
(-2, 2) 1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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26. Plot This Ordered Pair
(-3, -3)
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
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x

27. Plot This Ordered Pair
(-1, 2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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28. Plot This Ordered Pair
(1, -1)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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29. Plot This Ordered Pair
(2, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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30. Plot This Ordered Pair
(-3, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
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31. Credits
Clipart from “Microsoft Clip
Gallery” located on the Internet
at http://cgl.microsoft.com/
clipgallerylive/default.asp
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