Coordinate Geometry

Coordinate GeometryCoordinate Geometry

by Dhruv Verma by Dhruv Verma

X BX B

Copyright © 2000 by Monica Yuskaitis

DefinitionDefinition Grid – A pattern of horizontal and Grid – A pattern of horizontal and

vertical lines, usually forming vertical lines, usually forming squares.squares.


DefinitionDefinition Coordinate grid – a grid used to Coordinate grid – a grid used to

locate a point by its distances from locate a point by its distances from 2 intersecting straight lines.2 intersecting straight lines.

ABCDE

1 2 3 4 5

What are the coordinates

for the house?


DefinitionDefinition x axis – a horizontal number line x axis – a horizontal number line

on a coordinate grid.on a coordinate grid.

1 2 3 4 50 6 x


HintHint x is the shortest and likes to lie x is the shortest and likes to lie

down horizontally. down horizontally.

1 2 3 4 50 6 x


DefinitionDefinition y axis – a vertical number line on y axis – a vertical number line on

a coordinate grid.a coordinate grid.

12345

0

6

y


HintHint y is the tallest and stands upright or y is the tallest and stands upright or

vertically.vertically.

12345

0

6

y


DefinitionDefinition Coordinates – an ordered pair of Coordinates – an ordered pair of

numbers that give the location of a numbers that give the location of a point on a grid. point on a grid. (3, 4)(3, 4)

12345

0

6

1 2 3 4 50 6

(3,4)


HintHint The first number is always the x or first letter The first number is always the x or first letter

in the alphabet. The second number is always in the alphabet. The second number is always the y the second letter in the alphabet.the y the second letter in the alphabet.

1

32

45

0

6

1 2 3 4 50 6

(3,4)


How to Plot Ordered PairsHow to Plot Ordered Pairs Step 1 – Always find the x value Step 1 – Always find the x value

first, moving horizontally either right first, moving horizontally either right (positive) or left (negative).(positive) or left (negative).

1

32

45

0

6

1 2 3 4 50 6

(2, 3)

y

x


How to Plot Ordered PairsHow to Plot Ordered Pairs Step 2 – Starting from your new position Step 2 – Starting from your new position

find the y value by moving vertically find the y value by moving vertically either up (positive) or down (negative).either up (positive) or down (negative).

1

32

45

0

6

1 2 3 4 50 6

(2, 3)(2,3)y

x


How to Find Ordered PairsHow to Find Ordered Pairs Step 1 – Find how far over horizontally Step 1 – Find how far over horizontally

the point is by counting to the right the point is by counting to the right (positive) or the left (negative).(positive) or the left (negative).

1

32

45

0

6

1 2 3 4 50 6

(5, )

y

x


How to Find Ordered PairsHow to Find Ordered Pairs Step 2 – Now count how far Step 2 – Now count how far

vertically the point is by counting up vertically the point is by counting up (positive) or down (negative).(positive) or down (negative).

1

32

45

0

6

1 2 3 4 50 6

(5,4)

y

x


What is the ordered pair?What is the ordered pair?

1

32

45

0

6

1 2 3 4 50 6

(3,5)

y

x



1

32

45

0

6

1 2 3 4 50 6

(2,6)

y

x



1

32

45

0

6

1 2 3 4 50 6

(4,0)

y

x



1

32

45

0

6

1 2 3 4 50 6

(0,5)

y

x



1

32

45

0

6

1 2 3 4 50 6

(1,1)

y

x


Four Quadrants of Coordinate GridFour Quadrants of Coordinate Grid When the number lines are extended into When the number lines are extended into

the negative number lines you add 3 more the negative number lines you add 3 more quadrants to the coordinate grid.quadrants to the coordinate grid.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

y

x


Four Quadrants of Coordinate GridFour Quadrants of Coordinate Grid If the x is negative you move to If the x is negative you move to

the left of the 0.the left of the 0.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

x = -2y

x


Four Quadrants of Coordinate GridFour Quadrants of Coordinate Grid If the y is negative you move If the y is negative you move

down below the zero.down below the zero.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

y = -3y

x


How to Plot in 4 QuadrantsHow to Plot in 4 Quadrants Step 1 - Plot the x number first Step 1 - Plot the x number first

moving to the left when the moving to the left when the number is negative. number is negative.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -2)(-3, -2)y

x


How to Plot in 4 QuadrantsHow to Plot in 4 Quadrants Step 2 - Plot the y number moving Step 2 - Plot the y number moving

from your new position down 2 from your new position down 2 when the number is negative.when the number is negative.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -2)(-3, -2)

y

x


How to Plot in 4 QuadrantsHow to Plot in 4 Quadrants When x is positive and y is When x is positive and y is

negative, plot the ordered pair in negative, plot the ordered pair in this manner.this manner.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(2, -2)(2, -2)

y

x


How to Plot in 4 QuadrantsHow to Plot in 4 Quadrants When x is negative and y is When x is negative and y is

positive, plot the ordered pair in positive, plot the ordered pair in this manner.this manner.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-2, 2)(-2, 2)

y

x


Plot This Ordered PairPlot This Ordered Pair

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -3)(-3, -3)

y

x



-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-1, 2)(-1, 2)

y

x



-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(1, -1)(1, -1)

y

x



-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(2, -2)(2, -2)

y

x



-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -2)(-3, -2)

y

x


CreditsCredits

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

Education

Coordinate Geometry