Ordinate: Abscissa, Plotting Ordinates, Relation, Solved Examples

Ordinate represents the value of a coordinate on the y axis and Coordinate represents the position of the point along the line, arc, etc. The term "coordinate" represents the position of the point along the line, arc, etc., while the term "ordinate" represents the value of a coordinate on the y axis. There is a difference between two terms called coordinate and ordinate. 

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Meaning of Ordinate

Ordinate is the second component of an ordered pair. For example, if (x, y) is an ordered pair, then y is the ordinate here. An ordered pair is used to denote a point in the Cartesian plane. It is the second of the two terms (x, y) with which a point is defined, in a fixed Cartesian coordinate system of the plane. 

The first coordinate (x), in the plane, is called the abscissa. The Cartesian system uniquely designates each point in the XY plane by a pair of digital coordinates. These points are at distances from the two fixed axes, measured in the same unit of length.

Check Important Distance Formula and Derivation of Coordinate Geometry 

Example:

A point A of the Cartesian plane, of coordinates (6, 9), where 9 is the ordinate and a point B, of coordinates (7, 5), where 5 is the ordinate. In the case of point A, the ordinate is positive, so we will move in a positive direction on the y axis from the origin (0, 0) to 9 equal divisions but in the case of point B, we will move in a negative direction to 5 equal divisions.

The video below explains this:

Coordinate Geometry Detailed Video Explanation:

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Ordinate and Abscissa

The distance from a point to the y-axis scaled with the x-axis is called the abscissa or x-coordinate of the point. The distance from a point to the x-axis scaled with the y-axis is called the ordinate. They are called coordinates. 

The coordinates are written in brackets (), where the abscissa is written in the first position then the ordinate in the second position, separated by a comma. If x and y are respectively on the abscissa and on the ordinate, the position of the point P in the Cartesian plane is expressed by the pair of ordinates (x, y).

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Plotting Ordinates in Coordinate System

The 3 points (1, 2), (3, -3) and (-5,7) are far from the origin (0, 0). For point (1, 2), by plotting the ordinate, two parts are covered in the positive direction of the Y axis. Similarly, for point (3, 3) the ordinate covers three parts towards the negative direction of the 'Y axis, because here the ordinate is negative.

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Relation of Ordinate in the Coordinate

The ordinate depends entirely on the Y axis. So, while plotting it in a Cartesian plane, we have to move along or parallel to the positive or negative direction of the Y axis. This represents the relationship between the system of coordinates and the y axis.

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Things to Remember

• Ordinate value of all points on the x-axis is zero.
• The distance of a point from the x-axis is called ordinates or y-coordinates.
• The distance between two points which are on the same axis (x axis or y axis), is given by the difference between their ordinates if they are on the y axis, or by the difference between their abscissa if they are on the area on the x-axis.
• The horizontal line is called the x-axis and the vertical line is called the y-axis.
• The plane is called the Cartesian plane or coordinate plane, and the lines perpendicular to each other are called axes.
• The x coordinate of a point is called the abscissa.

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