Transcript Coordinate Geometry

Coordinate Geometry
Definition
 Grid – A pattern of horizontal and
vertical lines, usually forming
squares.
Definition
 Coordinate grid – a grid used to
locate a point by its distances from
2 intersecting straight lines.
A
B
C
D
E
What are the
coordinates
for the house?
1 2 3 4 5
Definition
 x axis – a horizontal number line
on a coordinate grid.
0 1 2 3 4 5 6
x
Hint
 x is the shortest and likes to lie
down horizontally.
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
Hint
 y is the tallest and stands upright or
vertically.
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). (2, 3)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
How to Plot Ordered Pairs

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 Find 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
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
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
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
Four Quadrants of Coordinate Grid
 If the x is negative you move to
the left of the 0. x = -2
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
Four Quadrants of Coordinate Grid
 If the y is negative you move
down below the zero. y = -3
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
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
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
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)
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
Plot This Ordered Pair
(-1, 2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
Plot This Ordered Pair
(1, -1)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
Plot This Ordered Pair
(2, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
Plot This Ordered Pair
(-3, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3