Post on 17-Jul-2020
transcript
Welcome to Bridge course Welcome to Bridge course
( )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
What is Analytical geometry?
A systematic study of geometry by the use of algebraby the use of algebra
La Geometric published in 1637
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 -
di tcoordinatesAbscissa
Ordinate
N
M
Q d tQuadrantsY
( )( )
III(+,+)(-,+)
XX’ OIII
III IVY’
(-,-) (+,-)Y
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 (?, ?)
Points on the axes
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.
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
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
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
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
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
Example Image of about the x axis isabout the x-axis isabout the y-axis is
is the image ofabout the origin
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)
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