René Descartes "I think, therefore I am." Founder of Analytic Geometry Cartesian philosophy, was based on skepticism use of reason through logical analysis

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Geometry& Algebra
United for the
First time This is the Real beauty of the Topic

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Yaam Bhumiti
Nirdeshak Bhumiti

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René Des ‘cartes’ “Cartes”ian
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.

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cogito ergo sum
I think therefore ,I am., Rene Descartes –
without whom –
we may not bedoing
Coordinate Geometry!

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

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After 2000 years of Euclidean Geometry This was the FIRST significant development by RENE DESCARTES ( French) in 17th Century,
Part of the credit goes to Pierre Farmat’s (French) pioneering work in analytic geometry In his manuscript "Varia opera mathematica",
("Introduction to Plane and Solid Loci").
Several decades after Descartes
Sir Isaac Newton (1640–1727) developed ten different coordinate systems.
Newton and Leibnitz used the polar coordinate system
It was Swiss mathematician Jakob Bernoulli (1654–1705)
who first used a polar co-ordinate system for calculus problems and coined the terms"pole" and "polar axis” Turning point in the
History of Mathematics

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Polar coordinate system
Parabolic coordinate system
Bipolar coordinates
Hyperbolic coordinates
Elliptic coordinates Cylindrical coordinate system
Spherical coordinate system
Parabolic coordinate system
Parabolic cylindrical coordinates
Paraboloidal coordinates
Oblate spheroidal coordinates
Prolate spheroidal coordinates
Ellipsoidal coordinates Elliptic cylindrical coordinates
Toroidal coordinates
Bispherical coordinates
Bipolar cylindrical coordinates
Conical coordinates
Flat-ring cyclide coordinates
Flat-disk cyclide coordinates
Bi-cyclide coordinates
Cap-cyclide coordinates Variety!!! Development of Maths

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E
x
t
r
a
D
o
s
e

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

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

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Use of Co-ordinate Geometry

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Use of Co-ordinate Geometry

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Use of Co-ordinate Geometry

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Use of Co-ordinate Geometry

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

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

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

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Practical Application: public double distance(Point p, Point q) { double dx = p.x - q.x; //horizontal difference double dy = p.y - q.y; //vertical difference double dist = Math.sqrt( dx*dx + dy*dy ); //distance using Pythagoras theorem return dist;} All computer programs written in
Java language,
uses distance between two points.

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Lettering with Grid

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

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A B C

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New topic Upgradation To Unit Shifted From New topic Area Of Triangle

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Introduction to Analytic Geometry

Dimensions :

Dimensions 1-D
2-D
3-D

1-D :

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

2-D: “THE” Distance formula :

2-D: “THE” Distance formula A B

2-D: “THE” Distance formula :

2-D: “THE” Distance formula A B

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From 3D to 2D

Distance between two points.In general, :

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

Distance between two points. :

Distance between two points. 5 18 3 17 A(5,3) B(18,17) 18 – 5 = 13 units 17 – 3 = 14 units AB2 = 132 + 142 Using Pythagoras’ Theorem, AB2 = (18 - 5)2 + (17 - 3)2 y x A ( 5 , 3 ) , B ( 18, 17 )
A ( x1 , y1 ) B ( x2 , y2 ) y2 - y1 = 17-3 X2 - x1 = 18-5

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Distance formula is nothing but
Pythagoras Theorem A B

The mid-point of two points. :

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

The mid-point of two points. :

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

Find the distance between the points (-1,3) and (2,-6) :

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

Topic Newly Introduced :

Topic Newly Introduced Area of triangle
when three vertices
are given.

Area :

Area Area of a Polygon.
Three points
A(Δ) = ½ [x1(y2-y3)+ x2 (y3-y1)+ x3 (y1-y2)]
The area of triangle ABC is given by
This formula may be extended to a n sided polygon with n vertices.
The area is then given by

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3 points are collinear
if AB+BC=AC then A-B-C. Collinear Points Show that the points A(-5,4) , B(-2,-2) ,
C(3 ,-12) are Collinear Points. If (3,7),(2,5),(-2,-3) are the Vertices
of a triangle.Show that these points
are Collinear Points.

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Revision of all topics
through
Co-ordinate Geometry All types of Triangles
and Quadrilaterals.
Collinearity
Area of Plane figures.
and C,G,I,O etc…

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Lesson Plan periods

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Long Answer Question:-
Sample Question 1 : Three vertices of a rectangle are
(3, 2), (– 4, 2) and (– 4, 5).
Plot these points and find the coordinates
of the fourth vertex.

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Time Management Matrix

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Human Function Curve

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Stress arises when: Demands > Resources ...Think ,Plan ,Execute and BE HAPPY

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