Coordinate geometry

Coordinate Geometry

by Monica Yuskaitis

Definition
 Grid – A pattern of horizontal and
vertical lines, usually forming
squares.

Copyright © 2000 by

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

Definition
 x axis – a horizontal number line
on a coordinate grid.

0 1 2 3 4 5 6

x

Hint
 x is the shortest and likes to lie
down horizontally.

0 1 2 3 4 5 6

x

Definition
 y axis – a vertical number line on
a coordinate grid.

y

6
5
4
3
2
1
0

Hint
 y is the tallest and stands upright or
vertically.

y

6
5
4
3
2
1
0

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

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

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

x



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



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

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

x

What is the ordered pair?

(3,5)
y

6
5
4
3
2
1
00 1 2 3 4 5 6

x


(2,6)
y

6
5
4
3
2
1
00 1 2 3 4 5 6

x


(4,0)
y

6
5
4
3
2
1
00 1 2 3 4 5 6

x


(0,5)
y

6
5
4
3
2
1
00 1 2 3 4 5 6

x


(1,1)
y

6
5
4
3
2
1
00 1 2 3 4 5 6

x

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

 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

x

 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

x

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

 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

 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

x

 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

Plot This Ordered Pair
(-3, -3)

y

3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3

x

(-1, 2)

y

3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3

(1, -1)

y

3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3

(2, -2)

y

3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3

(-3, -2)

y

3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3

Credits
Clipart from “Microsoft Clip
Gallery” located on the Internet
at http://cgl.microsoft.com/
clipgallerylive/default.asp


Coordinate geometry

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