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The position of a point of origin is the beginning or starting point, from where all the other points are taken into consideration. On a graph, this position is fixed, usually denoted as O, and acts as a definite reference point for the surrounding space. It is denoted as (0,0 ) on the graph. How far that point is from the origin determines the position of the coordinates.
The x and y-axis are equal to zero, and the x-axis and the y-axis intersect, and the point of intersection is 0.
Cartesian Plane
French mathematician Rene Descartes first introduced the concept of a Cartesian, where the two branches of algebra and geometry were put together by the plane or coordinate system.
How Does This System Work?
There is a straight line where integers are placed at an equal distance from a definite region.
The point from where the points are marked is the origin.
On the right-hand side, numbers are positive and the negative on the left of 0.
This straight line is a number line.
When two number lines are perpendicular, then a coordinate axis is formed.
What is The Cartesian Coordinate System?
A Cartesian coordinate system or coordinate system on a graph helps find the location of a point.
Pairs (x, y) are known as coordinates.
The X-axis is the horizontal line and is named X, X.
Y-axis is the vertical line and is named Y, Y.
‘O’ or the origin is the point of intersection of these two axes.
The coordinate plane is also called a 2-dimensional plane.
Quadrants of a Coordinate System
Dividing the Cartesian plane into four quadrants by the coordinate axes XX’ and YY’ are:
First quadrant – region XOY
Second quadrant- region X’OY
Third quadrant- region X’OY’
Fourth quadrant- region Y’OX
The four parts are called quadrants, and the plane divides into four parts. These parts are numbered I, II, III, and IV anticlockwise from OX. So, in a position of origin, the defining factor is the formation of a plane that consists of axes, and these quadrants and the plane is called the Cartesian plane or coordinate plane or the XY plane. The axis is called coordinate axes.
Sign Convention
On the X-axis: The ray OX is positive, OX’ is negative.
On the Y-axis- OY on Y-axis is positive, OY’ is negative.
(+, +) – I quadrant
(-, +) – II quadrant
(-, -) – III quardrant
(+, -) – IV quadrant
Cartesian Coordinates of a Point
In an ordered pair, the first number is the abscissa. The value of x in the ordered pair is called the abscissa which is the distance of a point on the plane from the y-axis. The second number in the ordered pair is the ordinate. It takes the value of y, and the ordinate is the distance of any point on the plane from the x-axis. For example, if the Cartesian coordinate is (2, 3), 2 represents the abscissa, and 3 illustrates the ordinate.
Taking a point on the X-axis, a distance of the point from the X-axis is O. The Y-coordinate on the X-axis is O. Hence, the coordinate of a point on the X-axis is given as (x, 0). Similarly, for a point on the Y-axis, the distance of the point from the Y-axis is O, i.e., the abscissa is zero.
Hence, the coordinates of a point on the Y-axis are (0, y).
If x=y, then (x,y) = (y,x)
If x ≠ y, then (x, y) ≠ (y, x)
( 0,0 ) are the coordinates of the origin.
Conclusion
Plotting of graph lines and points is done with the help of coordinate planes. Position of origin and coordinate planes hold a lot of importance in the real world. Arrangement of everyday furniture, mapping an area, locating aircraft, and conducting route maps can be done with the help of the coordinate plane.
