Math Doubts

Abscissa

The horizontal distance of a point from origin in two dimensional space is called the abscissa. It is also called as the $x$-coordinate.

Introduction

The abscissa is a geometric coordinate of a point, which is useful to know how far the point is from origin in horizontal direction in two dimensional Cartesian coordinate system.

abscissa or x coordinate

It is measured from origin in horizontal direction by comparing the number line on the $x$-axis. Hence, the abscissa is also called as the $x$-coordinate of the point.

While measuring the abscissa or $x$-coordinate of a point, the $y$-axis is considered as base line because the $y$-axis is passed through the origin in bi-dimensional Cartesian coordinate system.

Here, $P$ is a point on the plane and the horizontal distance of this point is measured as $d$ units from origin by comparing it with the number line on $x$-axis and also taking $y$-axis as base line.

The horizontal distance $d$ is called the abscissa or $x$-coordinate of the point $P$.

Steps

There are two simple steps to find the abscissa of any point in geometry.

  1. From any point, draw a perpendicular line to $x$-axis.
  2. The distance from origin to the intersecting point of the perpendicular line on $x$-axis is the abscissa or $x$-coordinate.

Example

Let’s learn how to measure the abscissa or $x$-coordinate of any point from an understandable example.

abscissa of two dimensional space

Let $A$, $B$, $C$ and $D$ be four points in a Bi-dimensional Cartesian coordinate system. Now, use the above two steps to determine the $x$-coordinate of each point.

  1. The abscissa of point $A$ is $4$.
  2. The $x$-coordinate of point $B$ is $-3$
  3. The abscissa of point $C$ is $-2$.
  4. The $x$-coordinate of point $D$ is $1$

Remember, the number line on the $x$-axis is considered while measuring the $x$-coordinate. So, no need to look at the number line on the $y$-axis.

Thus, the abscissa or $x$-coordinate of any point can be determined geometrically.

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