 # Ordinate

## Ordinate Meaning:

Ordinate is a term associated with the planar representation of a point in the cartesian coordinate system. The ordinate in the coordinate system refers to the y coordinate of any point in a cartesian plane. It refers to the perpendicular distance of the point from the X-axis and is parallel to Y-axis. The ordinate gives the horizontal distance of a point from the origin. For a set of points having the same ordinate and different abscissa, the line joining these points is a straight line parallel to X-axis.

### Cartesian Coordinate System:

The Cartesian coordinate system was developed by Rene Descartes, a great Mathematician. It is used to represent the position of an object along with its dimensions in a plane or space. The cartesian plane is a two-dimensional representation of the geometric figures. The two dimensions: length and width are represented by the X and Y coordinates respectively. Similarly in the cartesian space, the object is represented as a 3-dimensional view. The three dimensions of the object represented by X, Y, and  Z axes are length, width, and height respectively. The point in a cartesian plane is represented along with its coordinates as P (x, y). Similarly, a point in a cartesian space is represented as P (x, y, z).

### Plotting Ordinates in Coordinate System:

The cartesian plane consists of two axes X and Y mutually perpendicular to each other. In other words, the cartesian plane is a representation of two number lines mutually perpendicular to each other. The perpendicular axes divide the plane into four equal parts called the quadrants.

The ordinate in the coordinate system of a point gives the perpendicular distance of a point from the X-axis. i.e. the vertical distance of a point from the origin. If a point is represented by A (x, y), it is plotted on a cartesian plane at a distance x unit from the Y-axis and a distance of x units from the Y-axis. The point lies in the first quadrant if both x and y are positive. It lies in the second quadrant if x is negative and y is positive. The point is in the third quadrant if both x and y are negative. It is in the fourth quadrant if x is positive and y is negative.

An example of plotting a point P (2, 3) is shown in the figure below.

### The ordinate in Coordinate system examples:

1. Identify the ordinate and abscissa of the points represented by A, B, C, D, and E in the ordinate in coordinate system example given the figure. Also, state the quadrant to which the point belongs to.

## Solution:

 Point Ordinate Abscissa Quadrant A 4 4 I B -3 1 IV C -6 0 On Y axis D 1 -2 II E 2 1 I

1. Identify the ordinate in coordinate system examples and find the quadrant to which the following points belong to.

K (1, 3) L (-4, -5) M (-3, 2) N (4, -2) O (0, 0)

## Solution:

 Point Ordinate Quadrant K (1, 3) 3 I L (-4, -5) -5 IV M (-3, 2) 2 III N (4, -2) -2 II O (0, 0) 0 Origin

## Difference between Ordinate and Abscissa:

 Absissa Ordinate The term abscissa corresponds to the value represented by the x coordinate of a point. The term ordinate corresponds to the value of y coordinate of a point. The abscissa of a point is the perpendicular distance of the point from the Y-axis. The ordinate of a point is the perpendicular distance of the point from the X-axis. The abscissa gives the horizontal distance of a point. The ordinate gives the vertical distance of a point. For a set of points with the same abscissa and different ordinates, the line joining the points is a straight line parallel to Y-axis and perpendicular to X-axis. For a set of points with the same ordinate and different abscissa, the line joining the points is a straight line parallel to X-axis and perpendicular to Y-axis. If the abscissa is zero, the point lies on Y-axis If the ordinate is zero, the point lies on the X-axis. If the abscissa is positive, the point belongs to either the first or fourth quadrant. If the ordinate is positive, the point belongs to the first or second quadrant. If the abscissa is negative, the point belongs to either the second or third quadrant. If the ordinate is positive, the point belongs to the third or fourth quadrant. Ex: In the point P (3, -2), the abscissa is 3. Ex: In the point P (3, -2), plotting ordinates in the coordinate system is at the point -2.

### Fun quiz:

1. A point in the exterior of a plane closed geometric polygon is represented by the coordinates (5, 9). What is the ordinate of the point?

1. 5

2. 9

3. 59

1. Which one of the following is true while plotting ordinates in the coordinate system as 0?

1. The point lies on Y-axis

2. The point lies on X-axis

3. The point lies at the origin

1. If the point has a negative ordinate, the point in the cartesian plane may belong to ______

1. The first and third quadrant

2. The third and fourth quadrant

3. The first and fourth quadrant

4. The second and third quadrant