COORDINATE GEOMETRY

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Mind Map on COORDINATE GEOMETRY, created by Arkajyoti Bera on 02/06/2021.
Arkajyoti Bera
Mind Map by Arkajyoti Bera, updated more than 1 year ago
Arkajyoti Bera
Created by Arkajyoti Bera over 3 years ago
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COORDINATE GEOMETRY
  1. How do you accurately tell the position of your house to your friend?
    1. How do you locate your way to a landmark?
      1. How do you tell the position of a dot on a paper?
        1. How do you tell where you are sitting in a classroom?
          1. We can represent/locate a point in plane (called a Cartesian plane or a coordinate plane) by means of an ordered pair of real numbers, called the coordinates of that point. The branch of mathematics in which geometrical problems are solved using coordinate systems in known as Coordinate Geometry.
            1. Now, what is the Cartesian Plane?
              1. A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. The Cartesian plane extends infinitely in all directions.
                1. Here, the meeting point of two axes (plural of axis) is called origin.
                  1. "X-axis" is taken as the horizontal and extends positively in the right direction and negatively in the left direction, just like the number line. It is also called "abscissa".
                    1. "Y-axis" is taken as the vertical and extends positively in the upward direction and negatively in the downward direction, just like the number line rotated anticlockwise ?. It is also called "ordinate".
                      1. It is divided into four parts by the two axes extending in their respective directions endlessly. These parts are -
                        1. 1 st Quadrant (Quadrant I) - Both the "x" and "y" coordinates are positive
                          1. 2 nd Quadrant (Quadrant II) - Only the "y" coordinate is positive and the "x" coordinate is negative
                            1. 3 rd Quadrant (Quadrant III) - Both the "x" and the "y" coordinate are negative
                              1. 4 th Quadrant (Quadrant IV) - Only the "y" coordinate is negative and the "x" coordinate in positive
                                1. The Cartesian Plane looks like this -
                              2. How to locate a point on the Cartesian Plane?
                                1. We write the coordinates of the point we want to locate in this format -
                                  1. (x coordinate,y coordinate)
                                    1. Where, x-coordinate in the perpendicular distance of the point from the y-axis measured along the x-axis.
                                      1. And, y-coordinate is the perpendicular distance of the point from the x-axis measured along the y-axis.
                                        1. NOTE:- We must note that, the coordinates of the "origin" are (0,0). Also, the coordinates of the points lying on the x-axis are in the form of (X,0) and the points lying on y-axis are in the form of (0,Y).
                                        2. For Example -
                                          1. Plot the following points on a Cartesian Plane and tell on which Quadrant do they lie?
                                            1. A(2,-3) ; B(5,2) ; C(0,1) ; D(2,0) ; E(-4,-1) ; F(-3,4)
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