Today is our topic of discussion Rectangular Cartesian Coordinates .
Rectangular Cartesian Coordinates
We have been acquainted with the concept of plane in previous class. The surface of a table, the floor of a room, the surface of a book, even the paper on which we write down, each of them is a plane.
The surface of a football or the surface of a bottle are curved planes. In this part, the tricks of determining the proper position of any point lying on the plane will be discussed. For determining the proper position of any definite point, it is necessary to know the distance of the definite point from the straight line bisectors constructed on the plane. It is said as a reason that only a point can lie at any definite distance from two straight line bisectors.
If two such straight lines XOX’ and YOY’ are drawn that intersect each other at a right angle on any plane, XOX’ is called the x-axis, YOY’ is called the y-axis and the intersecting point ‘O’ is called the origin.
Now, let P be any point on the plane of the two axis. From point P, on XOX’ i.e., the x-axis and on YOY’ i.e., the y-axis, the perpendiculars are respectively PM and PN. Then the distance of point P from the y-axis = NP = OM = r is called the abscissa of P or r-coordinate.
Again, the distance of P from the x-axis =MP = ON = y is called the ordinate of P or y-coordinate. The abscissa and the Ordinate are jointly called the Coordinate. So, in the figure, the coordinate of P means the perpendicular distance of P from the y-axis and the x-axis and by denoting them as x and y, the coordinate of P is expressed by the symbol P(x,y) .
The coordinate index (x, y) means an ordered pair whose first element indicates the abscissa and the second element indicates the ordinate. So, if x ne y, by (x, y) and (y, x), two different points are meant. Therefore, the coordinate of any point depending on two axis intersecting each other at the right angle is called the Rectangular Cartesian Coordinates. If the point is placed at the right side of the y-axis, the abscissa will be positive and if it is placed at the left side, the abscissa will be negative.
Again, if the point is placed above the x-axis, the ordinate will be positive and if it is placed below, the ordinate will be negative. On the x-axis, the ordinate will be zero and on y-axis, the abscissa will be zero.
So, the positive abscissa and the ordinate of any point will be along OX and OY respectively or parallel to them. Similarly, the negative abscissa or the ordinate will be along O * X’ and O * Y’ respectively or parallel to them. By the two axis of the Cartesian coordinates, the plane is divided into XOY, YOX’, X’ * O * Y’ , Y’OX these four parts. Each of them is called a quadrant.
The quadrant XOY is taken as the first and by turns the second, the third and the fourth quadrant remain in anti-clockwise order. According to the sign of the point of the coordinate, the point lies on the different quadrants.
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