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What are
coordinates ?
Coordinatesare one of the
many methodsof locating a
point on aplain surface
2
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Here are
someways of
describing
the
location 3
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about 100meters
east of our
class
4
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situated atabout 60 km
north ofKuching
City
5
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column 3and row 3
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Arfillia Steward
Athirah Aisyah
Calvin Ilyas
Amir Najmi
ElaniFaizieSazwan
Geogina Ahmat Sorfina
Wyne Azwa Stanley
AsyrafRonaldoAlyana
Column1
Column2
Column3
Column4
Column5
Blackboard
ow
1
ow2
ow
3
ow4
2 RUBYS
(2010)
SITTING PLAN
7
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The
Cartesian
Plane
8
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CARTESIAN PLANE.
y
x6 5 4 3 2 1 0 1 2 3 4 5 6
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
xA(2, 3)
xB(3, 3)
xC(3, 0)
xD( 5, 2)
x
E ( 4, 4)x
F (0, 5)
xG(0, 0)
9
The Origin (0, 0)
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CARTESIAN PLANE.y
x6 5 4 3 2 1 0 1 2 3 4 5 6
7
6
5
4
3
2
1
0
-1
-2
-4
-5
-6
-7
-8
xA(2, 3)
xB(3, 4)
x
F( 3, 4)
xE( 6, 4)
xD (0, 5)
xC(3, 0)
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CARTESIAN PLANE.
y
x12 10 8 6 4 2 0 2 4 6 8 10 12
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
xA(4, 6)
xB(6, 6)
x
F( 6, 6)
xE( 12, 8)
xD (0, 10)
xC(6, 0)
11
Scale used
x - axis is 1 : 2
y - axis is 1 : 2
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CARTESIAN PLANE.
y
x12 10 8 6 4 2 0 2 4 6 8 10 12
18
15
12
9
6
3
0
-6
-9
-12
-15
-18
-21
-14
xA(4, 9)
xB(6, 12)
x
F( 6, 12)
xE( 12, 12)
xD (0, 15)
xC(6, 0)
xG (6, x )(6, 21)
12
x - axis is 1 : 2
y - axis is 1 : 3
Scale used
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THE
DISTANCEBETWEEN
TWO POINTS
13
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The DistanceBetween Two
points on The
CartesianPlane
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R(1, 4)xP(4, 0)x
x
y
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
and
Find the distance between :
PR = units2 24 3 16 9 25 5
4
3
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Q(1, 4)x
P(4, 0)x x
y
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
Find the distance between P(4, 0) and Q(1, 4)
PQ = 2 2
1 4 4 0
PQ = 22 43
PQ = 169
PQ = 25PQ = units5
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THE
COORDINATESOF
A
MIDPOINT
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To find the
coordinates of
the midpointof a line
joining twopoints on the
Cartesian
Plane . 18
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P(1, 5) and Q(5, 1)
x
y
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
What are the coordinates of the
mid-point of a line joining :
P(1, 5)
Q(5, 1)
(3, 3)
1 + 5 5 1he mid point of PQ ,2 2
6 6,
2 2
3, 3
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P(2, 6) and Q( 4, 2)
x
y
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
What are the coordinates of the
mid-point of a line joining :
P(2, 6)
Q( 4, 2)
( 1, 4)
2
26,
2
24
The coordinates of the mid-point of PQ
2
8,
2
2 4,1
20
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P( 3, 3) and Q(5, 3)
x
y
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
What are the coordinates of the
mid-point of a line joining :
P( 5, 3)
Q( 3, 3)
(1, 0)
2
33,
2
53
The coordinates of the mid-point of PQ
2
0,
2
2 0,1
21
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5 4 3 2 1 0 1 2 3 4 5
P( 2, 4) and Q(4, 6)
x
y5
4
3
2
1
1
2
3
4
5
What are the coordinates of the
mid-point of a line joining :
P( 4, 6)
P( 2, 4) (1, 5)
2
64,
2
42
The coordinates of the mid-point of PQ
2
10,
2
2 5,1
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10 8 6 4 2 0 2 4 6 8 10
P( 8, 12) and Q(4, 6)
x
y15
12
9
6
3
3
6
9
12
15
What are the coordinates of the
mid-point of a line joining :
Q(4, 6)
P( 8, 12)
2
612,
2
48
The coordinates of the mid-point of PQ
2
6,
2
4 3,2
( 2, 3)
23
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The End