Coordinate Geometry
Shirley Sides. 2006
Definition • Grid – A pattern of horizontal and vertical lines, usually forming squares.
• Coordinate grid – a grid used to locate a point by its distances from 2 intersecting straight lines. 6 5 4 3 2 1 00 1 2 3 4 5 6
Definition
Definition • x axis – a horizontal number line on a coordinate grid.
0 1 2 3 4 5 6
x
Hint • x ‘is a cross’ (across )
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
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).
y
6 5 (2, 3) 4 3 2 1 00 1 2 3 4 5 6 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
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).6 5 (5, 4) 4 y 3 2 1 00 1 2 3 4 5 6 x
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).
y
6 5 (5,4) 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
What is the ordered pair?
(2,6)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
x
What is the ordered pair?
(4,0)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
x
What is the ordered pair?
(0,5)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
x
What is the ordered pair?
(1,1)
y
6 5 4 3 2 1 00 1 2 3 4 5 6
x
• When the number lines are extended into the negative number lines you add 3 more quadrants to the coordinate grid.
Four Quadrants Grid
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
y
Four Quadrants 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
y
x
Four Quadrants 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
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 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 negative. y 3 2 (-3, -2) 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
How to Plot in 4 Quadrants
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
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 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
Plot This Ordered Pair (-3, -3)
3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 2 3
y
x
Plot This Ordered Pair (-1, 2)
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
y
Plot This Ordered Pair (1, -1)
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
y
Plot This Ordered Pair (2, -2)
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
y
Plot This Ordered Pair (-3, -2)
3 2 1 0 x -1 -2 -3 -3 -2 -1 0 1 2 3
y
Now try it yourself.
• Can you do 1 quadrant or all 4 quadrants? • Can you make a puzzle for someone else to do? • Can you find the message?