Transcript Grids, Coordinates, Ordered Number Pairs What They Are and How

Grids, Coordinates, Ordered
Number Pairs
What They Are and How They Work
Coordinates
Coordinates are “ordered pairs” of
numbers that we can use to help us find
things and go places.
They are called ordered because they
always come in the same order.
They look like this:(2,9) or (-3, 12) or
(10, -14)
We can use coordinates to find things, a
place on earth or on a map, to figure out
how to get from one point to another, and
to give us direction.
So how do the two numbers
help me find anything?
By themselves they don’t. For them to
work, you need a “grid.”
OK, so what’s a grid?
This is a grid.
So is this
g
f
e
d
c
b
a
X
1
2
3
4
5
6
We will talk about this type of grid later when
we learn about Graphs.
Lets look at the first grid type we
saw.
And if you add
numbers to the
grid,
it looks like this.
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
14
13
12
11
10
9
8
7
6
5
4
3
2
1
-1 1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11 12 13 14 15
Before we can
understand why
number on a grid are
so important, we
need to learn some
nomenclature.
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
14
13
12
11
10
9
8
7
6
5
4
3
2
1
-1 1
-2
-3
-4
-5
-6
-7
-8
-9
2
3
4
6
7
8
9
10 11 12 13 14 15
14
The two lines
that make the
grid have
names. They are
called the Axis.
13
12
11
10
This is X axis.
9
8
7
6
5
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
2
3
4
6
7
8
9
10 11
12
13
14
15
X
-2
-3
-4
-5
-6
This is the Y axis.
-7
-8
-9
-10
-11
-12
-13
-14
Y
The point where
the two lines cross
is (0,0).
14
13
Pay close attention
Notice that some of
the numbers are
positive numbers --
12
11
10
9
8
7
6
5
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
-2
-3
-4
-5
and some of the
numbers are negative
numbers.
-6
-7
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11
12
13
14
15
14
Now lets put a
box around the
grid.
13
12
11
10
9
+
8
7
6
5
4
3
2
1
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1 1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11 12 13 14 15
14
NO point has the
same coordinates as
any other point!
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2
13
12
11
10
9
+
8
7
6
5
4
3
2
1
-1 1
2
3
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
f
-12
-13
-14
R
4
6
7
8
9
10 11 12 13 14 15
So? What does this mean?
It means that if you know
the coordinates of a point
on the grid you can find it
quickly and easily!
How?
Like this: suppose you are given (7,5)
(14,-3) and (-4,-8)
all you need to remember is that you find
the first number along the X axis
(remember that is the side-to-side axis)
and the second number on the Y (updown) axis.
Let’s try it.
14
The secret of
using a grid is
to start at the
(0,0) point
13
Next move left or
right on the X axis
until you find the
first number in
your coordinate
pair.
12
11
10
9
8
7
6
5
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
-2
Then move up or
down on the Y axis
until you locate the
second number.
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11
12
13
14
15
14
Using our first
coordinates (7,5)
13
12
Then find 5 on
the Y.
11
10
9
8
7
6
First find 7 on the
X axis
5
Then connect
the dots.
(7,5)
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11
12
13
14
15
14
Using our second pair of
coordinates (14,-3)
13
12
11
First find 14 on the
X axis
10
9
8
7
6
5
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
2
3
4
6
7
8
9
10 11
12
13
14
15
-2
(14,-3)
-3
-4
Then find -3 on
the Y.
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
Then connect
the dots.
14
Using our last set of
coordinates (-4,-8)
13
12
Bingo! Now
you’ve got it!
11
10
9
8
7
Got what? I still don’t get
how this helps me find
anything.
6
First find -4 on the
X axis
5
4
3
2
1
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
-2
-3
-4
-5
-6
Then connect
the dots.
-7
(-4,-8)
-8
-9
-10
-11
-12
-13
-14
2
3
4
6
7
8
9
10 11
12
13
Then find –8 on
the Y.
14
15
So what does this have to do with
GEOGRAPHY?
14
13
12
11
10
What if I do
this!
9
8
7
6
5
4
3
Washington,
D.C.
2
1
-14 -13
-12
-11
-10 -9
-8
-7
-6
-5
-4
-3
-2
-1
-1 1
2
3
4
6
7
8
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
You
9
10
11
12
13
14
15
Do you see the grid?
Typical Graph
• This is an example of a
typical graph we are
all familiar with.
• The graph is made up
of different “points”
with lines that connect
the points.
Typical Graph
Y
(0,0)
(3,8)
(9,5)
• X value is
always stated
first
• Followed by the
Y value
• The “origin” is
the point where
X the 2 axes
intersect with a
value of (0,0)
The confusion comes
when we extend the
lines on the X and Y
axis around a sphere and
call them Longitude and
Latitude.
Longitude Lines go through the
poles.
Longitude and Latitude
Which is which?
Notice that these lines are the
hash marks on the X axis
X
Axis
Notice that these lines are the
hash marks on the X axis
X
Axis
Notice that these lines are the
hash marks on the X axis
14
13
12
11
10
9
8
7
6
5
4
3
2
1
X
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1 1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
2
3
4
6
7
8
9
10 11 12 13 14 15
Latitude lines go around the earth
like a belt.
Y axis
Latitude lines go around the earth
like a belt.
Y axis
How to remember which is
which. Think of Laddertude
On a ladder you go up the rungs.
Same with latitude.
See, Laddertude
The zero degrees mark of latitude
is the Equator, and the zero
degrees mark of longitude is the
Prime Meridian
0º, 0º
East West, North South on the
Earth
N
W
E
S
• Let each of the
four quarters
then be
designated by
North or South
and East or
West.
If you think about it for a minute,
you will see that the equator
divides the earth into halves. A
northern half, and a southern half.
And that Prime Meridian creates
East and West halves.
These two important lines divide the earth
into Hemi (which means ½ ) spheres.
Here is another image of the
Hemispheres
This makes it possible to think of
the earth like this:
(N, W)
(N, E)
• The N tells us we’re
north of the Equator.
The S tells us we’re
south of the Equator.
• The E tells us that
we’re east of the Prime
(S, W)
(S, E)
Meridian. The W tells
us that we’re west of the
Prime Meridian.
Two other important lines on
earth.
The Tropics.
Tropic Lines
How are longitude
and latitude
coordinates written
and what do they
mean?
Longitude and latitude are
measured in degrees, minutes,
and seconds and look like this.
The location of Lanier on Earth is:
29 º 44 30.14 N
95 º 29 18.40 W
We have learned that 0º of Latitude is
the Equator and 0º Longitude is the
Prime Meridian
• So we know that both latitude
and longitude are measured in
degrees.
• But how do you measure
between degrees?
Each DEGREE is
divided into MINUTES.
There are 60
MINUTES in each
DEGREE.
Each MINUTE is
divided into SECONDS.
There are 60
SECONDS in each
MINUTE.
NOW FOR PRACTICE
You will use your atlas to find
coordinates (longitude and
latitude) then answer the
question.
1 . In S. America, what country are you in
if you are at 10 degrees S, 50 degrees W
2. What African country are you in if you are
at 10º S, 40º E ?
3. What major city is the nearest to 30ºN, 90º
W?
4. What would you really need if you were
at 1º S, 3º W
5. What type of clothing would you need if
your position was 40ºN, 0º E in the winter?
6. What would your latitude be if you
were visiting Oslo, Norway?
7. How about Tokyo?
8. How about Perth, Australia?
Now do you see, if you have the
coordinates of a place on a
map, you can find the place
without spending hours looking
all over.
Wow, what a great idea!