Coordinate Geometry class 9th powerpoint presentation by akshat upadhyay
- 1. Developed by Pardeep Rani PGT Maths – JNV Chandigarh
- 2. CHAPTER - 3 COORDINATE GEOMETRY
- 3. CONTENT : • Why Coordinate Geometry ? • Activities from Routine Life • History of Coordinate Geometry • Cartesian System , Axes and Quadrants • Plotting of a Point in the Plane if its coordinates are given
- 4. Why Coordinate Geometry ? • Locate points on paper • Maps are based on coordinate geometry • Construction field • Plot graphs in finance • Various subjects (Astrophysics , Chemistry Molecules ) • Airplane Navigation 0 2 4 6 Series 1 Series 2 Series 3
- 5. Why Coordinate Geometry ? • Create animations & video games • MRI , Citi Scan , Xray in medical • In other words , we can say that Coordinate Geometry is useful in various fields of our routine life .
- 6. Situations from our Routine Life : • 1. In the adjoining figure , there is a main road running in the East-West direction and streets with numbering from West to East . Each street have house numbers marked on it .
- 7. Situations from our Routine Life : • To look for a friend’s house here , situated in the 2nd street and has the number 5 on it , first we will have to identify the 2nd street and then the house numbered 5 on it. Here , H shows the location of the house . • Similarly , P shows the location of the house corresponding to Street number 7 and House number 4.
- 8. LOCATION OF A POINT • Suppose you put a dot on a sheet of paper. If you have to tell its location , may be you reply : ‘the dot is in the upper/ lower half of the paper’ , or ‘ the dot is near the left / right edge of the paper’. But it will not fix the position of the dot precisely.
- 9. LOCATION OF A POINT • Whereas to fix the position of the dot you need two independent transformations e.g. the dot is nearly 5 cm away from the left edge of the paper and at a distance of 9 cm from the bottom line of the paper.
- 10. ACTIVITY FROM ROUTINE LIFE • To make it more interesting , we may perform the following classroom activity known as ‘Seating Plan’ : • Draw a plan of seating in your classroom , putting all the desks together , representing each desk by a square . Write the name of the student occupying the desk in each square. Sonia (S) is occupying the position (4,1). Filled(blue) block represents the position (5,3).
- 11. ACTIVITY FROM ROUTINE LIFE Thus , Position of each student in the classroom is described precisely by two independent informations : (i) the column in which she or he sits , (ii) the row in which she or he sits . From the above situations and activities , we can conclude that the position of any object lying in a plane can be presented with the help of two perpendicular lines. This idea gave rise to a very important branch of Mathematics known as Coordinate Geometry.
- 12. History of Coordinate Geometry Rene Descartes , the great French mathematician of the seventeenth century , solved the problem of describing the position of a point in a plane . His method was a development of the older idea of latitude and longitude . In honor of Descartes, the system used for describing the position of a point in a plane, is also known as the Cartesian System.
- 13. Cartesian System • As you have already studied in the chapter Number System , On the number line ,equal distances from fixed point (origin-0) are marked positively in one direction and negatively in the other. The point in the positive direction at a distance of r units from the origin represents the number r and the point in the negative direction at a distance of r units from the origin represents the number –r as shown in the figure :
- 14. AXES IN THE CARTESIAN PLANE • Descarte invented the idea of placing two such lines perpendicular to each other on a plane such that one of them is horizontal and the other vertical, named as X’X (x-axis)and YY’ (y- axis) respectively as described in the figure :
- 15. AXES AND QUADRANTS OF A PLANE • Observe that the axes (plural of axis) divide the plane into four parts named as quadrants numbered as I , II , III and IV anticlockwise from OX. So plane consisting of the axes and the quadrants is called Cartesian or the Coordinate Plane or the xy-plane. The axes are called coordinate axis.
- 16. SIGNS OF x and y in QUADRANTS • Quadrant I is represented by XOY , here x and y both are positive . • Quadrant II is represented by X’OY , here x is negative and y is positive. • Quadrant III is represented by X’OY’ , here x and y both are negative. • Quadrant IV is represented by XOY’ , here x is positive and y is negative.
- 17. Abscissa & Ordinate • In the adjoining graph , you find that : • (i) The perpendicular distance of P from y-axis measured along the positive direction of the x-axis is PN = OM = 4 units • (ii) The perpendicular distance of P from x-axis measured along the positive direction of the y-axis is PM = ON = 3 units
- 18. Abscissa & Ordinate • (iii)The perpendicular distance of Q from y-axis measured along the negative direction of the x-axis is OR = SQ = 6 units • The perpendicular distance of Q from x-axis measured along the negative direction of the y- axis is OS = RQ = 2 units • Here , the x – coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis. For the point P , it is 4 and for Q it is -6. the x – coordinate is called the Abscissa .
- 19. Abscissa & Ordinate • The Y – coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis. For the point P , it is 3 and for Q it is -2. the y – coordinate is called the Ordinate . • In stating the coordinates of a point in the coordinate plane, the x- coordinate comes first , and then the y-coordinate . Coordinates are placed in open ( round) brackets . • Hence , the coordinates of P are (4,3) and Q are (-6,-2).
- 20. • Every point on the x- axis has zero distance from x – axis , so the y-coordinate of every point lying on x-axis is always zero i.e. coordinate of every point on x-axis are of the form (x,0). Similarly ,coordinates of every point on y-axis are of the form (0,y). • Coordinates of Origin Origin has zero distance from both the axes so that its abscissa and ordinate are both zero. Therefore , the coordinates of origin are (0,0). (0,0)
- 21. • EXAMPLE : In the adjoining figure, • (i) The coordinates of B are (-5,2). • (ii) The coordinates of C are (5,-5). • (iii) The point identified by the coordinates (-3,-5) is E . • (iv) The point identified by the coordinates (2,-4) is G. • (v) The abscissa of the point D is 6. • (vi) The ordinate of the point H is -3 . • (vii) The coordinates of the point L are (0,5). • (viii) The coordinates of the point M are (-3,0).
- 22. Plotting of a Point in the Plane • Let the coordinates of the given point be (3,5). • We know that x-coordinate i.e. abscissa represents distance of point from y- axis , so first we will move 3 units from origin towards positive direction of x - axis and then y-coordinate i.e. ordinate being distance of point from x – axis , we will move 5 units from that position towards positive direction of y – axis. This location will represent the point (3,5). • Similarly , we can plot point (5,- 4) and as many points as we want .
- 23. • Example : Plot the points (5,0), (0,5), (2,5),(5,2) ,(-3,-5) , (-3,5) , (5,-3) and (6,1) in the Cartesian plane. • From the above example and many more like this , we can conclude that the position of (x,y) is different from the position of (y,x) for x ≠ y . i.e. • (x,y) ≠ (y,x) for x ≠ y and (x,y) = (y,x) for x = y
- 24. Independent Practice for the students : • In which quadrant or on which axis do each of the points (-2,4) , (3,-1) , (-1,0) , (1,2) , (-3,-5) and (4,0) lie ? Verify your answer by locating them on the Cartesian plane.