Coordinate Geometry

1
Coordinate Geometry

• Shirley Sides.
• 2006

2
Definition

• Grid A pattern of horizontal and vertical
  lines, usually forming squares.

3
Definition

• Coordinate grid a grid used to locate a point
  by its distances from 2 intersecting straight
  lines.

6
5
4
3
2
1
0
1
2
3
4
5
0
6
4
Definition

• x axis a horizontal number line on a
  coordinate grid.

x
1
2
3
4
5
0
6
5
Hint

• x is a cross (across ?)

x
1
2
3
4
5
0
6
6
Definition

• y axis a vertical number line on a coordinate
  grid.

6
5
y
4
3
2
1
0
7
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
0
1
2
3
4
5
0
6
8
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
0
1
2
3
4
5
0
6
9
How to Plot Ordered Pairs

• Step 1 Always find the x value first, moving
  horizontally either right (positive) or left
  (negative).

6
5
(2, 3)
4
y
3
2
1
0
x
1
2
3
4
5
0
6
10
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
5
(2, 3)
4
(2,3)
y
3
2
1
0
x
1
2
3
4
5
0
6
11
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).

6
5
(5, 4)
4
y
3
2
1
x
0
1
2
3
4
5
0
6
12
How to Find Ordered Pairs

• Step 2 Now count how far vertically the point
  is by counting up (positive) or down (negative).

6
5
(5,4)
4
y
3
2
1
0
x
1
2
3
4
5
0
6
13
What is the ordered pair?
(3,5)
6
5
4
y
3
2
1
0
x
1
2
3
4
5
0
6
14
What is the ordered pair?
(2,6)
6
5
4
y
3
2
1
0
x
1
2
3
4
5
0
6
15
What is the ordered pair?
(4,0)
6
5
4
y
3
2
1
0
x
1
2
3
4
5
0
6
16
What is the ordered pair?
(0,5)
6
5
4
y
3
2
1
0
x
1
2
3
4
5
0
6
17
What is the ordered pair?
(1,1)
6
5
4
y
3
2
1
0
x
1
2
3
4
5
0
6
18
Four Quadrants 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
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
19
Four Quadrants Grid

• If the x is negative you move to the left of the
  0.

x -2
y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
20
Four Quadrants Grid

• If the y is negative you move down below the
  zero.

y -3
y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
21
How to Plot in 4 Quadrants

• Step 1 - Plot the x number first moving to the
  left when the number is negative.

• (-3, -2)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
22
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
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
23
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
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
24
How to Plot in 4 Quadrants

• When x is negative and y is positive, plot the
  ordered pair in this manner.

y
3
2

• (-2, 2)

1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
25
Plot This Ordered Pair

• (-3, -3)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
26
Plot This Ordered Pair

• (-1, 2)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
27
Plot This Ordered Pair

• (1, -1)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
28
Plot This Ordered Pair

• (2, -2)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
29
Plot This Ordered Pair

• (-3, -2)

y
3
2
1
x
0
-1
-2
-3
-2
-1
0
1
2
-3
3
30
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?