Coordinate Geometry - GCSE / Cambridge O-level
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Transcript of Coordinate Geometry - GCSE / Cambridge O-level
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Coordinate GeometryCoordinate Geometry
by Monica Yuskaitis by Monica Yuskaitis
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DefinitionDefinition
GridGrid ± ± A pattern of horizontal andA pattern of horizontal andvertical lines, usually formingvertical lines, usually formingsquares.squares.
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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?
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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
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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
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DefinitionDefinition y axisy axis ± ± a vertical number line ona vertical number line on
a coordinate grid.a coordinate grid.
12
345
0
6
y
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HintHint y is the tallest and stands upright or y is the tallest and stands upright or
vertically.vertically.
12
345
0
6
y
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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)
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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)
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Copyright © 2000 by Monica Yuskaitis
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
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Copyright © 2000 by Monica Yuskaitis
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
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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
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Copyright © 2000 by Monica Yuskaitis
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
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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
![Page 15: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/15.jpg)
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What is the ordered pair?What is the ordered pair?
1
3
2
45
0
6
1 2 3 4 50 6
(2,6)
y
x
![Page 16: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/16.jpg)
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What is the ordered pair?What is the ordered pair?
1
3
2
45
0
6
1 2 3 4 50 6
(4,0)
y
x
![Page 17: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/17.jpg)
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What is the ordered pair?What is the ordered pair?
1
3
2
45
0
6
1 2 3 4 50 6
(0,5)
y
x
![Page 18: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/18.jpg)
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What is the ordered pair?What is the ordered pair?
1
3
2
45
0
6
1 2 3 4 50 6
(1,1)
y
x
![Page 19: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/19.jpg)
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Copyright © 2000 by Monica Yuskaitis
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
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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
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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
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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
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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
![Page 24: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/24.jpg)
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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
![Page 25: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/25.jpg)
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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
![Page 26: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/26.jpg)
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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
![Page 27: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/27.jpg)
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Plot This Ordered Pair Plot This Ordered Pair
-2
0
-1
12
-3
3
-2 -1 0 1 2-3 3
((--1, 2)1, 2)y
x
![Page 28: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/28.jpg)
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Plot This Ordered Pair Plot This Ordered Pair
-2
0
-1
12
-3
3
-2 -1 0 1 2-3 3
(1,(1, --1)1)
y
x
![Page 29: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/29.jpg)
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Plot This Ordered Pair Plot This Ordered Pair
-2
0
-1
12
-3
3
-2 -1 0 1 2-3 3
(2,(2, --2)2)
y
x
![Page 30: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/30.jpg)
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Plot This Ordered Pair Plot This Ordered Pair
-2
0
-1
12
-3
3
-2 -1 0 1 2-3 3
((--3,3, --2)2)
y
x
![Page 31: Coordinate Geometry - GCSE / Cambridge O-level](https://reader034.fdocuments.net/reader034/viewer/2022051203/577d35c91a28ab3a6b91690a/html5/thumbnails/31.jpg)
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CreditsCredits
Clipart from ³Microsoft Clip
Gallery´ located on the Internetat http://cgl.microsoft.com/
clipgallerylive/default.asp