Coordinate Geometry

Coordinate Geometry - Transcript

Coordinate Geometry
by Monica Yuskaitis
Copyright © 2000 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
What are the
coordinates
for the house?
Copyright © 2000 by
Monica Yuskaitis
Definition
 x axis – a horizontal number line
on a coordinate grid.
1 2 3 4 50 6 x
Copyright © 2000 by
Monica Yuskaitis
Hint
 x is the shortest and likes to lie
down horizontally.
1 2 3 4 50 6 x
Copyright © 2000 by
Monica Yuskaitis
Definition
 y axis – a vertical number line on
a coordinate grid.
1
2
34
5
0
6
y
Copyright © 2000 by
Monica Yuskaitis
Hint
 y is the tallest and stands upright or
vertically.
1
2
34
5
0
6
y
Copyright © 2000 by
Monica Yuskaitis
Definition
 Coordinates – an ordered pair of
numbers that give the location of a
point on a grid. (3, 4)
1
2
34
5
0
6
1 2 3 4 50 6
(3,4)
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.
1
3
2
4
5
0
6
1 2 3 4 50 6
(3,4)
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).
1
3
2
4
5
0
6
1 2 3 4 50 6
(2, 3)
y
x
Copyright © 2000 by
Monica Yuskaitis
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).
1
3
2
4
5
0
6
1 2 3 4 50 6
(2, 3)
(2,3)y
x
Copyright © 2000 by
Monica Yuskaitis
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).
1
3
2
4
5
0
6
1 2 3 4 50 6
(5, )
y
x
Copyright © 2000 by
Monica Yuskaitis
How to Find Ordered Pairs
 Step 2 – Now count how far
vertically the point is by counting up
(positive) or down (negative).
1
3
2
4
5
0
6
1 2 3 4 50 6
(5,4)
y
x
Copyright © 2000 by
Monica Yuskaitis
What is the ordered pair?
1
3
2
4
5
0
6
1 2 3 4 50 6
(3,5)
y
x
Copyright © 2000 by
Monica Yuskaitis
What is the ordered pair?
1
3
2
4
5
0
6
1 2 3 4 50 6
(2,6)
y
x
Copyright © 2000 by
Monica Yuskaitis
What is the ordered pair?
1
3
2
4
5
0
6
1 2 3 4 50 6
(4,0)
y
x
Copyright © 2000 by
Monica Yuskaitis
What is the ordered pair?
1
3
2
4
5
0
6
1 2 3 4 50 6
(0,5)
y
x
Copyright © 2000 by
Monica Yuskaitis
What is the ordered pair?
1
3
2
4
5
0
6
1 2 3 4 50 6
(1,1)
y
x
Copyright © 2000 by
Monica Yuskaitis
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.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
y
x
Copyright © 2000 by
Monica Yuskaitis
Four Quadrants of Coordinate Grid
 If the x is negative you move to
the left of the 0.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
x = -2y
x
Copyright © 2000 by
Monica Yuskaitis
Four Quadrants of Coordinate Grid
 If the y is negative you move
down below the zero.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
y = -3y
x
Copyright © 2000 by
Monica Yuskaitis
How to Plot in 4 Quadrants
 Step 1 - Plot the x number first
moving to the left when the
number is negative.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-3, -2)y
x
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.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-3, -2)
y
x
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.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(2, -2)
y
x
Copyright © 2000 by
Monica Yuskaitis
How to Plot in 4 Quadrants
 When x is negative and y is
positive, plot the ordered pair in
this manner.
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-2, 2)
y
x
Copyright © 2000 by
Monica Yuskaitis
Plot This Ordered Pair
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-3, -3)
y
x
Copyright © 2000 by
Monica Yuskaitis
Plot This Ordered Pair
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-1, 2)
y
x
Copyright © 2000 by
Monica Yuskaitis
Plot This Ordered Pair
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(1, -1)
y
x
Copyright © 2000 by
Monica Yuskaitis
Plot This Ordered Pair
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(2, -2)
y
x
Copyright © 2000 by
Monica Yuskaitis
Plot This Ordered Pair
-2
0
-1
1
2
-3
3
-2 -1 0 1 2-3 3
(-3, -2)
y
x
Copyright © 2000 by
Monica Yuskaitis
Credits
Clipart from “Microsoft Clip
Gallery” located on the Internet
at http://cgl.microsoft.com/
clipgallerylive/default.asp