31503881
Description
Mind Map by Arkajyoti Bera, updated more than 1 year ago
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Created by Arkajyoti Bera
over 3 years ago
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COORDINATE GEOMETRY
- How do you accurately
tell the position of your
house to your friend?
- How do you locate your
way to a landmark?
- How do you tell the position
of a dot on a paper?
- How do you tell where
you are sitting in a
classroom?
- 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.
- Now, what is the Cartesian
Plane?
- 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.
- Here, the meeting point of two axes (plural of axis) is called origin.
- "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".
- "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".
- It is divided into four parts by the two axes extending in their
respective directions endlessly. These parts are -
- 1 st Quadrant (Quadrant I) - Both the "x" and "y"
coordinates are positive
- 2 nd Quadrant (Quadrant II) - Only the "y" coordinate
is positive and the "x" coordinate is negative
- 3 rd Quadrant (Quadrant III) - Both the "x" and the
"y" coordinate are negative
- 4 th Quadrant (Quadrant IV) - Only the "y"
coordinate is negative and the "x" coordinate in
positive
- The Cartesian Plane looks like this
-
- 1 st Quadrant (Quadrant I) - Both the "x" and "y"
coordinates are positive
- 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.
- How to locate a point on the Cartesian Plane?
- We write the coordinates of the point we want to
locate in this format -
- (x coordinate,y coordinate)
- Where, x-coordinate in the perpendicular distance of
the point from the y-axis measured along the x-axis.
- And, y-coordinate is the perpendicular distance of
the point from the x-axis measured along the y-axis.
- 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).
- 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).
- For Example -
- Plot the following points on a Cartesian Plane
and tell on which Quadrant do they lie?
- A(2,-3) ; B(5,2) ; C(0,1) ; D(2,0) ; E(-4,-1) ;
F(-3,4)
- A(2,-3) ; B(5,2) ; C(0,1) ; D(2,0) ; E(-4,-1) ;
F(-3,4)
- Plot the following points on a Cartesian Plane
and tell on which Quadrant do they lie?
- Where, x-coordinate in the perpendicular distance of
the point from the y-axis measured along the x-axis.
- (x coordinate,y coordinate)
- We write the coordinates of the point we want to
locate in this format -
- Now, what is the Cartesian
Plane?
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