1. "I think, therefore I am." René Descartes Founder of Analytic Geometry
Descartes lived during the early 17th century. Descartes found a way to describe curves in an arithmetic way. He developed a new method called coordinate geometry, which was basic for the future development of science.

2. “Cartes”ian René Des ‘cartes’ Co Ordinate System Geometry and the Fly
One morning Descartes noticed a fly walking
across the ceiling of his bedroom.
As he watched the fly, Descartes began to think of how the fly's path could be described without actually tracing its path. His further reflections about describing a path by means of mathematics led to La Géometrie  and Descartes's invention of coordinate geometry.

3. Algebraic Equation in Geometry
x – 2y = 1
Line
Geogebra
X—2y = 1 is a line in Geometry

4. History of Mathematics
Turning point in the
History of Mathematics
After years of Euclidean Geometry This was the FIRST significant development by RENE DESCARTES ( French) in 17th Century,
Part of the credit goes to Pierre Fermat’s (French) pioneering work in analytic geometry.
Sir Isaac Newton (1640–1727) developed ten different coordinate systems.
It was Swiss mathematician Jakob Bernoulli (1654–1705) who first used a polar co-ordinate system for calculus
Newton and Leibnitz used the polar coordinate system

5. ┴ GRID Two intersecting Number lines determine
Two intersecting line determine a plane.
Two intersecting Number lines determine
a Co-ordinate Plane/system. or
Cartesian Plane.
Rectangular Co-ordinate system.
Two Dimensional orthogonal
Co-ordinate System or XY-Plane
GRID

6. Use of Co-ordinate Geometry
Cell Address is (D,3) or D3

7. Use of Co-ordinate Geometry

8. Use of Co-ordinate Geometry

9. Use of Co-ordinate Geometry

10. Use of Co-ordinate Geometry
MAP R A D

11. Use of Co-ordinate Geometry Pixels in Digital Photos
Each Pixel uses x-y
co-ordinates
Pixels in Digital Photos

12. Coordinate geometry is also applied in scanners
Coordinate geometry is also applied in scanners. Scanners make use of coordinate geometry to reproduce the exact image of the selected picture in the computer. It manipulates the points of each piece of information in the original documents and reproduces them in soft copy.
Thus coordinate geometry is widely used without our knowing..

14. The screen you are looking at is a grid of thousands of tiny dots called pixels that together make up the image

15. Practical Application:
All computer programs written in
Java language,
uses distance between two points.

16. Lettering with Grid

17. II I IV III Frame of reference Half Plane origin Vertical Above X-Axis
Horizontal
Left of Y-axis
origin
Right of Y-axis
Terms
Abscissa
Ordinate
Ordered Pair
Quadrants
Sign –Convention IV
Below X-Axis
III

18. Co-ordinate Geometry Statistics Linear Equations Mensuration Graph
Construction
Trigonometry
Points & lines
Congruency
Similarity
Pythagoras Theorem

19. Dimensions
1-D
2-D
3-D a b y x y x z

20. 1-D
Distance Formula
| b-a | or
| a-b | a b

21. 2-D: “THE” Distance formulaB A

22. 2-D: “THE” Distance formulaB A

23. From 3D to 2D

24. The modern applications of MapQuest, Google Maps, and most recently, GPS devices on phones, use coordinate geometry.
Satellites have taken a 3-d world and made it a 2-d grid in which locations have numbers and labels.
The GPS system takes these numbers and labels and maps out directions, times and mileage using the satellite given locations to tell you how to get from one place to another, how long it will be and how much time it will take!
Amazing!!

25. Distance between two points. In general,y
B(x2,y2)
AB2 = (y2-y1)2 + (x2-x1)2 y2
Hence, the formula for Length of AB or Distance between A and B is
Length = y2 – y1 y1
A(x1,y1)
Length = x2 – x1 x x1 x2

26. Distance between two points.
X2 - x1 = 18-5
A ( 5 , 3 ) , B ( 18, 17 )
A ( x1 , y1 ) B ( x2 , y2 )
y2 - y1 = 17-3 y
Using Pythagoras’ Theorem,
AB2 = (18 - 5)2 + (17 - 3)2
B(18,17) 17
AB2 =
17 – 3 = 14 units 3
A(5,3)
18 – 5 = 13 units x 5 18

27. Distance formula is nothing but
Pythagoras Theorem B A

28. The mid-point of two points.
Look at it’s horizontal length y
B(18,17)
Mid-point of AB y2
Look at it’s vertical length
Formula for mid-point is y1
A(5,3) x x1 x2

29. The mid-point of two points.
Look at it’s horizontal length y
Mid-point of AB
B(18,17) 17
= 11.5
(11.5,
10)
Look at it’s vertical length 10 3
A(5,3)
11.5
(18,3)
= 10 x 5 18

30. Find the distance between the points (-1,3) and (2,-6)
y2—y1= -6-3= -9
x2—x1=2--(--1)= 3
(-1, 3) (2, -6)
(x1 , y1 ) (x2 ,y2 )
AB= 9.49 units (3 sig. fig)