Transcript Coordinate Geometry

Content
Cartesian Coordinates
History
Activity 1
Objectives:
 Know what is a Cartesian
coordinate system
 Give the Cartesian coordinates
of a point.
Activity 2
Activity 3
 Locate and plot a point with
given Cartesian coordinates
 Graph ordered pairs.
History
Rene Descarte (1596 – 1650) was a French
philosopher, mathematician and a scientist.
The story goes that one day when Descartes
was sick in bed, he saw a fly crawling on the
tiled ceiling.
He wondered, “ Exactly where is that fly?”
Descartes imagined a grid superimposed on the
ceiling.
It made him realized that he could explain where the fly was by
defining a pair of numbers that can be read off with reference to
two number lines . Today, this grid was known as Cartesian
Coordinate system.
Home
Today , the coordinate system helps us
to ….
Application
in 3D space
locate seats in
cinema
locate objects
using GPS
tracking system
Home
Activity 1
This is the seating arrangement of a class, the teacher
locate the position of student A,B, C using a pair of
numbers (x,y). How did she locate their positions ?
A (3,3)
C
B (6,2)
C (2,5)
A
B
1
2
3
4
5
Front of the class
6
7
8
Well, the first number indicates the position of the required
row from the left and , the second number ,the position up
the row. Thus, student C’s seat was at (2,5), B’s seat was at
(6,2) and A’s seat was at (3,3) .
C
5
4
A
3
B
2
1
1
2
3
4
5
6
7
8
Home
What is a Cartesian
Coordinate Plane ?
The vertical
number line is
called the y axis.
y
A pair of real
number is called
an ordered pair.
5
4
The point of
intersection of the
two number lines is
called ORIGIN.
A (2, 3)
3
2
1
−5 −4 −3
−2
−1 0
−1
−2
B (5, 3)
−3
−4
5
x
1
2
3
4
5
The horizontal
number line is
called the x axis.
What is an ordered pair ?
• When we say the point A has coordinates:
( 2, 3 )
Number 2 is called
Number 3 is called
x -coordinate
y -coordinate
What do point A of x coordinate and y coordinate mean?
A has y coordinate = 3
Draw a horizontal line
from A, we will reach the
y axis at the number 3
y
A has x-coordinate = 2.
Draw a line vertical line
from A, we will reach the
x-axis at 2.
5
4
A (2, 3)
3
2
1
−5
−4
−3
−2
−1 0
−1
−2
−3
B (5, 3)
−4
5
1
2
3
4
5
6
7
x
Activity 2
Can you name the ordered pair for the following
places near your school? To check your answers
, click on the icon.
Activity 2
Did you get it right ? Try the next icon …..
(3,3)
To quit, click on
Activity 2
Did you get it right ? Try the next icon …..
(1-4)
To quit, click on
Activity 2
Did you get it right ? Try the next icon …..
(1,4)
To quit, click on
Activity 2
Did you get it right ? Try the next icon …..
(0,0)
To quit, click on
Activity 2
Did you get it right ? Try the next icon ….
(-1,4)
To quit, click on
Activity 2
Did you get it right ? Try the next icon …..
(7,-5)
To quit, click on
Activity 2
Did you get it right ? Try the next icon …..
(-6,-5)
To quit, click on
Activity 2
Good Job and well done !!
(1,4)
(-5,7)
(-1,4)
(3,3)
(0,0)
(1,- 4)
(-6,-5)
Home
Activity 3
Click on the following website to
play the game.
http://www.shodor.org/interactivate/activities/MazeGame/
Instructions : Key in
the x and y coordinates
so that the robot can
travel safely to the
green location by
avoiding all the mine
fields.
Please be patient while
being connected to
internet.
Home
E-learning Task
Materials :
1 piece of graph paper
Instructions:
1. Write your name, index number and class.
2. Write the answers for Question 1 and 2 at the back
of the graph paper.
3. For Question 3 plot your points on your graph
paper and answer the question.
4. Hand in your work on 4th Feb, Monday to your
Maths teacher.
Question 1
(i) Write down the
coordinates of the following
points:
(a)N
(b) P
(c) S (d) U
(ii) Write down the points
denoted by the following:
(d) (-2,3) (e) (3,4) (f) (1,-1)
(iii) Identify the figure if you
plot and join the following
points ( 1,-1) , (1,5) ,(-3,-1)
Question 2
PQRS is a square.
Write down the
coordinates of P.
Question 3
Draw the x-y axis by
using 1 cm to
represent 1 unit on
both axes as shown.
y
7
6
5
4
3
2
1
-4
-3 -2
-1 0
1
2
3
4
5
x
Plot and join the
points in the given
order:
(1,5),(3,5),(1,7),(1,3)
(-2,3), (-1,2), (3,2),
(4,3), (1,3). Identify
the figure that you
have obtained.
Congratulations !!!
You had completed the assignment !