Understanding Ordinate and Its Role in the Coordinate Plane
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 the 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 the 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 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 of 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
Identify the ordinate and abscissa of the points represented by A, B, C, D, and E in the coordinate system example given in the figure. Also, state the quadrant to which the point belongs.
Solution:
Identify the ordinate in coordinate system examples and find the quadrant to which the following points belong.
K (1, 3) L (-4, -5) M (-3, 2) N (4, -2) O (0, 0)
Solution:
Difference between Ordinate and Abscissa
Fun Quiz
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?
5
9
59
Which one of the following is true while plotting ordinates in the coordinate system as 0?
The point lies on Y-axis
The point lies on X-axis
The point lies at the origin
If the point has a negative ordinate, the point in the cartesian plane may belong to ______
The first and third quadrant
The third and fourth quadrant
The first and fourth quadrant
The second and third quadrant
Importance of Ordinates in Maths
Ordinates usually refer to the perpendicular distance of the point from the X-axis and is parallel to the Y-axis. It gives a horizontal distance of a point from the origin. For any given set of points having the same ordinate but different abscissa, the line joining these points is a straight line that’s parallel to the X-axis. All students of Maths need to know about ordinates and coordinates before they sit for Coordinate Geometry exams. All students who need to do well in exams as well as pursue Maths, later on, can refer to the page on Vedantu. Maths is one subject that will always prove to be beneficial for all students as it has implications throughout a student's life.
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Vedantu has Ordinate on its platform which all Maths students can read and understand. It has compact information on Ordinates that all students can understand and apply. This material has been provided free of cost so that students do not hesitate before reading from the page.
FAQs on What Is an Ordinate in Maths?
1. What is an ordinate in coordinate geometry?
In coordinate geometry, the ordinate refers to the y-coordinate of a point on a Cartesian plane. It represents the perpendicular distance of that point from the horizontal X-axis, measured parallel to the vertical Y-axis. In any ordered pair (x, y), the ordinate is always the second value, which is 'y'.
2. What is the y-coordinate of a point also known as?
The y-coordinate of a point in a Cartesian coordinate system is also known as the ordinate. For context, the x-coordinate is known as the abscissa.
3. What is the main difference between an abscissa and an ordinate?
The primary difference between an abscissa and an ordinate lies in which axis they relate to and their position within a coordinate pair (x, y).
- Ordinate: This is the y-coordinate (the second value in the pair). It measures the point's vertical distance from the X-axis.
- Abscissa: This is the x-coordinate (the first value in the pair). It measures the point's horizontal distance from the Y-axis.
4. How do you find the ordinate for a given point, for example, P(4, -7)?
To find the ordinate of any point, you simply identify the second number in its coordinate pair (x, y). For the point P(4, -7), the first number, 4, is the abscissa. The second number, -7, is the ordinate. Therefore, the ordinate of point P is -7.
5. What does the sign of an ordinate (positive, negative, or zero) tell you about a point's position?
The sign of the ordinate gives precise information about a point's vertical position relative to the X-axis:
- A positive ordinate (y > 0) indicates the point is located above the X-axis (in either Quadrant I or II).
- A negative ordinate (y < 0) indicates the point is located below the X-axis (in either Quadrant III or IV).
- A zero ordinate (y = 0) indicates the point lies directly on the X-axis itself.
6. Is the ordinate the same thing as the Y-axis?
No, the ordinate is not the same as the Y-axis, which is a common misconception. The Y-axis is the entire vertical reference line in the Cartesian plane. In contrast, the ordinate is a single numerical value (the y-coordinate) that specifies a point's exact vertical distance from the X-axis.
7. Why is a coordinate pair (x, y) called an 'ordered pair' and how does this relate to the ordinate?
A coordinate pair is called an 'ordered pair' because the sequence of the numbers is fundamentally important for defining a point's unique location. The first number is always the abscissa (x-coordinate), and the second is always the ordinate (y-coordinate). The ordinate's fixed position as the second value is crucial. For instance, the point (2, 9) has an ordinate of 9, while the point (9, 2) has an ordinate of 2. These are two completely different points, proving that the order cannot be changed.
8. What is the ordinate of a point that lies on the X-axis?
The ordinate of any point that lies on the X-axis is always zero. This is because the ordinate measures the vertical distance from the X-axis. If a point is on the axis itself, its vertical distance from it is zero. For example, the point (5, 0) lies on the X-axis.
