Slide 1: Smt. T.S.Popat
Head Mistress
Sanghavi K.M.High School
Gujarati Medium Co-ordinator
B.O.S.
MATHS
Slide 2: Co-ordinate Geometry Chapter No. (G, 6) 1 4 5 3 2 7 9 8 6 1 5 4 3 2 6 7
Slide 3: René Descartes "I think, therefore I am." Founder of Analytic Geometry Cartesian philosophy, was based on skepticism use of reason through logical analysis
Slide 4: Geometry& Algebra
United for the
First time This is the Real beauty of the Topic
Slide 5: Yaam Bhumiti
Nirdeshak Bhumiti
Slide 6: 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.
Slide 7: cogito ergo sum
I think therefore ,I am., Rene Descartes –
without whom –
we may not bedoing
Coordinate Geometry!
Slide 8: Algebraic Equation in Geometry
x – 2y = 1 Line X—2y = 1 is a line in Geometry Geogebra
Slide 9: 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
Slide 10: 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
Slide 11: E
x
t
r
a
D
o
s
e
Slide 12: 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
Slide 13: Use of Co-ordinate Geometry Cell Address is (D,3) or D3
Slide 14: Use of Co-ordinate Geometry
Slide 15: Use of Co-ordinate Geometry
Slide 16: Use of Co-ordinate Geometry
Slide 17: Use of Co-ordinate Geometry
Slide 18: Use of Co-ordinate Geometry R
A
D
A
R
MAP R
A
D
A
R
Slide 19: Use of Co-ordinate Geometry Pixels in Digital Photos Each Pixel uses x-y
co-ordinates
Slide 21: The screen you are looking at is a grid of thousands of tiny dots called pixels that together make up the image
Slide 22: 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.
Slide 23: Lettering with Grid
Slide 24: 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
Slide 25: A B C
Slide 26: New topic Upgradation To Unit Shifted From New topic Area Of Triangle
Slide 28: 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
Slide 33: 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
Slide 36: 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
Slide 43: 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.
Slide 44: 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…
Slide 45: Lesson Plan periods
Slide 46: 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.
Slide 47: Time Management Matrix
Slide 48: Human Function Curve
Slide 49: Stress arises when: Demands > Resources ...Think ,Plan ,Execute and BE HAPPY