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Rectangular Coordinate System

A rectangular coordinate system is formed by one horizontal and one vertical line, that intersect at the origin (0, 0). The intersection point is also called as origin. The two lines are called coordinate axes or simply axes. In geometry, a rectangular coordinate system is used to study relationship between variables.
The perpendicular axes divide the plane into four quadrants, which are numbered counter-wise from I (one) to IV (four). Each point in the plane can be identified by a pair of numbers. The first number measure distance from x-axis and second from y-axis. The second name for the x-axis is abscissa and for y-axis is ordinate.
In other words, first coordinate of ordered pair is abscissa and the second coordinate is the ordinate.

                                       quadrant 4

This system is made up of 2 number lines x axis and y axis. These two axes meet at origin (0, 0). The x coordinate is also called as abscissa and the y coordinate is known as ordinate. The order pair (x, y) tells us how far we move from the origin.

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Terms Used in Rectangular Coordiante System

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X-Axis: X-axis is a horizontal line and the equation for the x-axis is y = 0.

Y-Axis: This is called as vertical line. The equation for the y-axis is x = 0.

Origin: The point where the two axes (X axis and Y axis intersects). At origin both x and y coordinates are zero (0, 0).

Ordered pairs: Every point in a coordinate plane is named by pair of numbers these are written in parenthesis and separated by comma. The ordered pair of origin is given as (0, 0).

X coordinate or abscissa:  The first number in parenthesis is called as x coordinate. It indicates the amount of movement along x axis. If the number is positive the movement is to right and if the number is negative then movement is to the left from origin. If point is (2, 5) then abscissa is 2 .

Y coordinate or ordinate:  The second number in parenthesis (ordered pair) is called y ordinate. It indicates the amount of movement that is perpendicular to the x axis. If the ordinate is positive then the movement is above the x axis and if the ordinate is negative then the movement is below the x axis. If point given is (-3, 4) then abscissa is -3.

Quadrants:  In a Cartesian Coordinate system the X axis and Y axis divides the plane into 4 regions called Quadrants. They are indicated by Roman numeral I, II, III, IV. 


Example of Rectangular Coordinate System

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Example:  Plot the coordinates: A (2, 3), B (-3, 1) and C (-1.5, -2.5)

Solution:  Since the point A is (2, 3) so 2 is abscissa and 3 is ordinate since both ordered pairs are positive so it lies in quadrant I. To plot it, from origin we move to right 2 units then move up 3 units.

Since the point is B (- 3, 1) then abscissa is -3 and ordinate is 1 since x coordinate is negative and y coordinate is positive so the point lies in II quadrant. To plot it from origin we move 3 units left then move 1 unit up.

Since point is C (-1.5, -2.5) then abscissa is -1.5 and ordinate is -2.5. Since both coordinates is negative so the point lies in III quadrant. To plot the point from origin we 1.5 units left and then move 2.5 units down .

                               

Rectangular Coordinate System Example

                



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