What Is the Abscissa Definition Formula and Solved Examples
In the coordinate system, the term “abscissa” refers to the x -coordinate of the point (x, y). In short, the distance along the x-axis is called the abscissa. There is a difference in two terms i.e coordinate and ordinate. The term “coordinate” represents the position of the point along the line in the cartesian system, whereas the term “ordinate” represents the value of a coordinate on the y-axis. After going through this article, the student will be able to learn what is abscissa in Maths, what is abscissa and ordinate with an example, and how to plot the abscissa in the coordinate system in detail.
Abscissa Meaning
The abscissa is the first component in an ordered pair. Suppose, (x, y) is an ordered pair, then x is the abscissa here. An ordered pair is used to represent a point in the Cartesian plane. It is the first of the two terms (x, y) by which a point is defined, in a system of fixed Cartesian Coordinate planes. The first coordinate value (x), in the plane, is known as the abscissa. The Cartesian system designates each point in the XY plane, uniquely, by a pair of numerical coordinate values. These points are at the distances from the two fixed axes which are measured in the same unit of length.
What is Abscissa in Maths?
The abscissa meaning in maths is defined as the distance of a point from the y-axis on a graph in the Cartesian coordinate system. It is measured parallel to the x-axis. For example, a point having coordinates (5,3) here 5 is its abscissa. It is the measurement along the y-axis which is parallel with the x-axis to point. Abscissa differs as we move on the x-axis from left or right. Its value is always 0 for all the points on the y- axis.
Abscissa Example
Let’s take an example of a point A in the Cartesian plane, having coordinates (5, 8), where 5 is the abscissa and a point B, having coordinates (-5, 6), where -5 is the abscissa. In the case of point A, the abscissa is positive, so we have to move towards a positive direction on the x-axis from the origin (0, 0) at 5 equal divisions but in the case of point B, we have to move towards a negative direction at 5 equal divisions.
Ordinate Abscissa
The distance of a point measured from the y-axis along the x-axis is called the abscissa or x-coordinate of the point. The distance of a point measured from the x-axis along the y-axis is called ordinate. The abscissa and ordinate all together are known as coordinates.
The coordinates values are written in the brackets (). The abscissa is written in the first position and the ordinate in the second position, they both are separated by a comma. If x and y are abscissa and ordinate respectively, then the location of the point P in the Cartesian plane is represented by the ordered pair (x, y).
In the above diagram coordinate point (12, 5) is shown. Here first value 12 is called abscissa and the second value 5 is called ordinate.
The Abscissa of a Point
The abscissa of a point is defined as the signed measure of its projection on the primary axis (known as the x-axis), whose absolute value is the distance between the projection and the origin of the axis. The sign of abscissa is given by the location of the relative point to the origin. The x - coordinate of a point is the perpendicular distance from the y-axis measured along the x-axis.
Relation of Abscissa Ordinate in the Coordinate System
The ordinate value depends entirely on the Y-axis. So when we plot it in a Cartesian plane, we have to move along or parallel to the positive or negative direction of the Y-axis. This is the relation between the coordinate system and the y-axis.
Representation of a Point on the Cartesian Plane
With the help of coordinate axes, we can describe any point in the plane using an ordered pair of numbers. In the given below figure, point A is represented by an ordered pair (x, y) where x is the abscissa and y is the ordinate of the point.
Note:
x-coordinate (abscissa): Distance along X axis.
y-coordinate (ordinate): Distance along Y-axis.
Origin is at zero distance from both the axes so the value of abscissa and ordinate are zero. Therefore, (0, 0) is the coordinates of the origin.
The coordinates of a point on the x-axis is in the form of (x, 0) and that of the point on the y-axis is in the form of (0, y).
Solved Examples
1.What is the Abscissa of Point P(-4,6)?
Sol: As we know abscissa is the first value in an ordered pair. Here the first value is -4. Hence -4 is the abscissa of the point P(-4,6).
2. If the Value of the X-coordinate is 6 and the Y-coordinate is 8. Find the Value of Abscissa and Ordinate.
Sol: We know that x-coordinate is known as abscissa, so its value is 6. Also, y-coordinate is known as ordinate and its value is 8.
FAQs on Abscissa in Coordinate Geometry
1. What is the abscissa in mathematics?
The abscissa is the x-coordinate of a point in the Cartesian coordinate system. It represents the horizontal distance of a point from the origin along the x-axis.
- In a point written as (x, y), the first value x is the abscissa.
- If x is positive, the point lies to the right of the origin.
- If x is negative, the point lies to the left of the origin.
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. Together, they form an ordered pair (x, y) in the Cartesian plane.
- Abscissa (x): Horizontal position from the origin.
- Ordinate (y): Vertical position from the origin.
3. How do you find the abscissa of a point?
To find the abscissa of a point, identify the first number in its ordered pair (x, y).
- Step 1: Write the coordinates of the point.
- Step 2: The first value represents the x-coordinate.
4. What does the abscissa represent on a graph?
The abscissa represents the horizontal position of a point on a graph. It measures how far left or right a point is from the origin along the x-axis.
- Positive abscissa → right side of the y-axis.
- Negative abscissa → left side of the y-axis.
- Zero abscissa → point lies on the y-axis.
5. Can the abscissa be zero?
Yes, the abscissa can be zero if the point lies on the y-axis. When x = 0, the point has no horizontal displacement from the origin.
- Example: The point (0, 5) has abscissa 0.
- All points on the y-axis have abscissa equal to zero.
6. What is an example of abscissa in coordinate geometry?
An example of abscissa is the x-value in the coordinate pair (2, −3).
- Point: (2, −3)
- Abscissa (x-coordinate): 2
- Ordinate (y-coordinate): −3
7. Why is the abscissa important in graphing?
The abscissa is important in graphing because it determines a point’s horizontal location on the coordinate plane. Without the x-coordinate, the exact position of a point cannot be plotted.
- It helps define linear equations like y = mx + c.
- It is used to identify intercepts such as the x-intercept.
- It allows accurate plotting of functions and data points.
8. What is the abscissa of a point on the y-axis?
The abscissa of a point on the y-axis is 0. Any point located on the y-axis has no horizontal distance from the origin.
- General form: (0, y)
- Example: (0, −7) has abscissa 0.
9. What is the abscissa of a point on the x-axis?
The abscissa of a point on the x-axis is the x-value itself, while its ordinate is 0. Any point on the x-axis has coordinates of the form (x, 0).
- Example: (5, 0) has abscissa 5.
- Example: (−3, 0) has abscissa −3.
10. Is abscissa always written first in coordinates?
Yes, the abscissa is always written first in an ordered pair (x, y). The standard format in coordinate geometry places the x-coordinate before the y-coordinate.
- Correct format: (x, y)
- Example: (4, −2) → abscissa = 4
