Coordinate Geometry
by Monica Yuskaitis
Definition Grid – A pattern of horizontal and vertical lines, usually forming squares.
Copyright © 2000 by Monica Yuskaitis
Definition Coordinate grid – a grid used to locate a point by its distances from 2 intersecting straight lines.
A B C D E 1 2 3 4 5
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What are the coordinates for the house?
Definition x axis – a horizontal number line on a coordinate grid.
0 1 2 3 4 5 6
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x
Hint x is the shortest and likes to lie down horizontally.
0 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
x
Definition y axis – a vertical number line on a coordinate grid.
y
6 5 4 3 2 1 0
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Hint y is the tallest and stands upright or vertically.
y
6 5 4 3 2 1 0
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
x
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
Copyright © 2000 by Monica Yuskaitis
How to Plot 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
Copyright © 2000 by Monica Yuskaitis
How to Find Ordered Pairs
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
Copyright © 2000 by Monica Yuskaitis
x
What is the ordered pair?
(3,5)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
x
What is the ordered pair?
(2,6)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
x
What is the ordered pair?
(4,0)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
x
What is the ordered pair?
(0,5)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
x
What is the ordered pair?
(1,1)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
Four Quadrants of Coordinate Grid If the x is negative you move to the left of the 0. x = -2
3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
x
Four Quadrants of Coordinate Grid If the y is negative you move down below the zero. y = -3
3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
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 x 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
How to Plot in 4 Quadrants Step 2 - Plot the y number moving from your new position down 2 when the number is negative.
y 3 2 (-3, -2) 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
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
Copyright © 2000 by Monica Yuskaitis
x
How to Plot in 4 Quadrants When x is negative and y is positive, plot the ordered pair in this manner. y (-2, 2)
3 2 1 x 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
Plot This Ordered Pair (-3, -3)
3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
x
Plot This Ordered Pair (-1, 2)
3 2 1 x 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
Plot This Ordered Pair (1, -1)
3 2 1 x 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
Plot This Ordered Pair (2, -2)
3 2 1 x 0 -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
Plot This Ordered Pair (-3, -2)
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
Copyright © 2000 by Monica Yuskaitis
y
Credits
Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/ clipgallerylive/default.asp
Copyright © 2000 by Monica Yuskaitis