welcome to bridge course - kea | home · rené descartes (1596 –1650) cartesian i can place 2...
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Welcome to Bridge course Welcome to Bridge course
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( )René Descartes (1596 – 1650) Cartesian I can place 2
number lines
Cartesian coordinate number lines
one perpendicular
system
perpendicular to the other so h h h f that the path of the flying bird can be set
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What is Analytical geometry?
A systematic study of geometry by the use of algebraby the use of algebra
La Geometric published in 1637
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Coordinates of a pointY3
ctio
n
Y-axis : Y’OY
1
2
vedirec
X-axis : X’OX
XX’ O
1 2 3 41234
1
+vX axis : X OX
Origin
1 2 3 4
+ve direction
-1-2-3-4
-1
ection
Y’-ve direction
-2
-3 -ve
dire
Y 3 -
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di tcoordinatesAbscissa
Ordinate
N
M
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Q d tQuadrantsY
( )( )
III(+,+)(-,+)
XX’ OIII
III IVY’
(-,-) (+,-)Y
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E lExampleY
3
1
2
(2,1)Abcissa
XX’ O
1 2 3 41234
1
1 2 3 4-1-2-3-4
-1Ordinate
Y’
-2
-3
(-3,-2)
(? ?)Y 3 (?, ?)
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Points on the axes
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Image of a pointImage of a point
N
MO
T i h i f i b
O
To write the image of a point about th i l b
To write the image of a point about the y‐axis replace x by – x the x‐axis replace y by – y.
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Image about the origin
To write the image of a point about the origin replace x by – x and y by – y y y y
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Example
If th b i f i t If the abscissa of a point is three times the ordinate then
Gi diti i Given condition is
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Example
If the abscissa of the point If the abscissa of the point is square of its ordinate then
Given condition is Given condition is
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The point (3, 2) moves a distance 5 units in the negative direction of gthe x-axis. From its new position it turns to the direction of the turns to the direction of the negative y-axis and moves a distance 7 units Write the new distance 7 units. Write the new position of the point
2 32 3M2
5N
5
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A point lies on the x-axis at a distance 3 units from the point distance 3 units from the point (- 2, 0). The position of the point iis
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Example Image of about the x axis isabout the x-axis isabout the y-axis is
is the image ofabout the origin
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ExampleThe image of (x, y) about the g ( , y)x-axis and y-axis respectively are (2 - 3) and (- 2 3) Find are (2, 3) and ( 2, 3). Find x and y.image about x axis is (2 3)image about x-axis is (2, - 3)image about y-axis is (- 2, 3)
y = 3
g y ( , )
x = 2 (2, 3)
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THANK YOU THE WOODS ARE LOVELY THE WOODS ARE LOVELY ““THE WOODS ARE LOVELY THE WOODS ARE LOVELY DARK AND DEEPDARK AND DEEPBUT I HAVE PROMISES BUT I HAVE PROMISES TO KEEP TO KEEP AND AND MILES TO GO MILES TO GO BEFORE I SLEEP BEFORE I SLEEP BEFORE I SLEEP BEFORE I SLEEP AND AND MILES TO GO MILES TO GO BEFORE I SLEEP”BEFORE I SLEEP” R b FBEFORE I SLEEP”BEFORE I SLEEP”‐ Robert Frost