Coordinate Geometry - GCSE / Cambridge O-level

8/8/2019 Coordinate Geometry - GCSE / Cambridge O-level

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Coordinate GeometryCoordinate Geometry

by Monica Yuskaitis by Monica Yuskaitis



Copyright © 2000 by Monica Yuskaitis

DefinitionDefinition

GridGrid ± ± A pattern of horizontal andA pattern of horizontal andvertical lines, usually formingvertical lines, usually formingsquares.squares.




DefinitionDefinition Coordinate gridCoordinate grid ± ± a grid used toa grid used to

locate a point by its distances fromlocate a point by its distances from2 intersecting straight lines.2 intersecting straight lines.

ABC

DE

1 2 3 4 5

What are the

coordinates

for the house?




DefinitionDefinition x axisx axis ± ± a horizontal number linea horizontal number line

on a coordinate grid.on a coordinate grid.

1 2 3 4 50 6x




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

down horizontally.down horizontally.

1 2 3 4 50 6x




DefinitionDefinition y axisy axis ± ± a vertical number line ona vertical number line on

a coordinate grid.a coordinate grid.

12

345

0

6

y




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

vertically.vertically.

12

345

0

6

y




DefinitionDefinition CoordinatesCoordinates ± ± an ordered pair of an ordered pair of

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

12

345

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 alwaysin the alphabet. The second number is always

the y the second letter in the alphabet.the y the second letter in the alphabet.

1

3

2

45

0

6

1 2 3 4 50 6

(3,4)




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

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

1

3

2

45

0

6

1 2 3 4 50 6

(2, 3)

y

x




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

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

1

3

2

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 1Step 1 ± ± Find how far over horizontallyFind how far over horizontally

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

1

3

2

45

0

6

1 2 3 4 50 6

(5, )

y

x




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

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

1

3

2

45

0

6

1 2 3 4 50 6

(5,4)

y

x




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

1

3

2

45

0

6

1 2 3 4 50 6

(3,5)

y

x





1

3

2

45

0

6

1 2 3 4 50 6

(2,6)

y

x





1

3

2

45

0

6

1 2 3 4 50 6

(4,0)

y

x





1

3

2

45

0

6

1 2 3 4 50 6

(0,5)

y

x





1

3

2

45

0

6

1 2 3 4 50 6

(1,1)

y

x




Four Quadrants of Coordinate GridFour Quadrants of Coordinate GridWhen the number lines are extended intoWhen the number lines are extended into

the negative number lines you add 3 morethe negative number lines you add 3 morequadrants 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 toIf 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 moveIf 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 1Step 1 -- Plot the x number firstPlot the x number first

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

-2

0

-1

12

-3

3

-2 -1 0 1 2-3 3

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

x




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

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

-2

0

-1

12

-3

3

-2 -1 0 1 2-3 3

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

y

x




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

negative, plot the ordered pair innegative, plot the ordered pair inthis 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 isWhen x is negative and y is

positive, plot the ordered pair in positive, plot the ordered pair inthis 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 Pair Plot 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

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

y

x




CreditsCredits

Clipart from ³Microsoft Clip

Gallery´ located on the Internetat http://cgl.microsoft.com/

clipgallerylive/default.asp

Documents

Coordinate Geometry - GCSE / Cambridge O-level