What Is the Ordinate of a Point with Formula and Examples
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 Ordinate in Coordinate Geometry Explained
1. What is an ordinate in coordinate geometry?
An ordinate is the y-coordinate of a point in the Cartesian coordinate system. In an ordered pair written as (x, y), the first value is the abscissa (x-coordinate) and the second value is the ordinate (y-coordinate).
- It represents the vertical distance from the x-axis.
- If y is positive, the point lies above the x-axis.
- If y is negative, the point lies below the x-axis.
2. What is the difference between abscissa and ordinate?
The abscissa is the x-coordinate, while the ordinate is the y-coordinate of a point in the Cartesian plane. In the ordered pair (x, y):
- Abscissa → horizontal distance from the y-axis.
- Ordinate → vertical distance from the x-axis.
3. How do you find the ordinate of a point?
To find the ordinate, read the second value in the ordered pair (x, y). The steps are:
- Write the coordinates of the point.
- Identify the second number (y-value).
4. What does a positive or negative ordinate mean?
A positive ordinate means the point lies above the x-axis, while a negative ordinate means it lies below the x-axis. Specifically:
- If y > 0, the point is above the x-axis.
- If y < 0, the point is below the x-axis.
- If y = 0, the point lies on the x-axis.
5. What is the ordinate of a point on the x-axis?
The ordinate of any point on the x-axis is 0. This is because every point on the x-axis has coordinates of the form (x, 0), meaning there is no vertical distance from the x-axis.
6. What is the ordinate of a point on the y-axis?
The ordinate of a point on the y-axis can be any real number, while the abscissa is 0. Points on the y-axis are written as (0, y), so the ordinate is simply the y-value itself. For example, in (0, 6), the ordinate is 6.
7. How is ordinate used in graphing a linear equation?
In graphing a linear equation, the ordinate represents the y-value corresponding to a chosen x-value. For a linear equation y = mx + c:
- Choose a value of x (abscissa).
- Substitute into the equation.
- Calculate y, which is the ordinate.
8. What is meant by the ordinate of the origin?
The ordinate of the origin is 0. The origin in coordinate geometry is the point (0, 0), where both the abscissa and ordinate are zero.
9. Can the ordinate be a fraction or decimal?
Yes, the ordinate can be any real number, including fractions and decimals. For example:
- In (2, 1/2), the ordinate is 1/2.
- In (−3, 4.75), the ordinate is 4.75.
10. Why is the ordinate important in coordinate geometry?
The ordinate is important because it determines the vertical position of a point in the Cartesian plane. It helps in:
- Identifying the quadrant of a point.
- Graphing equations and functions.
- Calculating slope, distance, and midpoint.
