If you are searching for help on how to get the coordinates of a point you have arrived at the correct place. Check out the complete details about a point x coordinate, y coordinate in the following sections of this page. Get to know what is meant by coordinates and how to find the coordinates of a point in a coordinate geometry along with few examples to get a better idea of the concept.
Coordinates of a Point Definition
Coordinates are nothing but a set of real numbers that represent the exact position of a point in a cartesian plane, Generally, a two-dimensional coordinate plane has two axes namely the x-axis, y-axis. The two coordinates of a point are abscissa or x coordinate, ordinate or y coordinate.
Steps to Find Coordinates of a Point in a Plane
In order to find the coordinates of a point, you must have a coordinate plane. The concept of finding the point coordinates is quite easy.
- As a first step, check out the coordinate graph having both horizontal and vertical lines.
- Find in which quadrant the given point falls and based on that you will get the signs of coordinates of a point.
- Draw two dotted perpendicular lines from the point to the x-axis, y-axis.
- Measure the distance between the dotted line meeting point on the x-axis and consider it as x coordinate.
- Likewise, measure the distance from the origin to the dotted line meeting point on the y-axis.
- Take it as y coordinate.
- Then, write your point as (x_coordinate_value, y_coordinate_value).
Point Coordinates
In any two dimensional plane, each point has two coordinates. The first coordinate is called the x coordinate which is measured along the x-axis. The second coordinate of the point is called the y coordinate which is measured along the y-axis. More details about the coordinates are mentioned below.
Abscissa: It is defined as the first number of a point which is present before the comma and after the opening parenthesis. It is also known as the x coordinate. Its value can be positive or negative. If the abscissa is zero, then we call it a point on the y-axis. Usually, the x coordinate value is measured along the x-axis.
Ordinate: The second number of an ordered pair is called the ordinate. It is also called the y coordinate. It is available after the comma and before the closing parenthesis, it can be negative or positive. If the y coordinate value is zero in a point, then it is called the point on the x-axis. Generally, its value is measured along the y-axis.
Solved Examples
1. In the adjoining figure, XOX’ and YOY’ are the co-ordinate axes. Find out the coordinates of points P, Q, R, S. And also write x coordinate, y coordinate of each point?
Solution:
To find the point P:
Point P is the fourth quadrant. So its abscissa is positive, the ordinate is negative.
The perpendicular distance of the point from the x-axis is 1 unit, y-axis also 1 unit.
So, x coordinate is 1, y coordinate is -1.
Therefore, point P (1, -1)
To locate the point Q:
As Q is in the first quadrant, its coordinates are positive.
The perpendicular distance between point and origin on the x-axis is 2 units, on the y-axis is 4 units.
So, abscissa is 2, ordinate is 4
Therefore, Q (2, 4)
To locate point R:
The point R is the second quadrant. So, the R x coordinate is negative and the y coordinate is positive.
The perpendicular distance of the point on the x-axis is 5 units, the y-axis is 3 units.
X coordinate is -5, y coordinate is 3.
Therefore R (-5, 3)
To find the point S:
The point S is located in the fourth quadrant.
The perpendicular distance of the point from the x-axis is 6 units and it is positive.
The perpendicular distance along the y-axis is 3 units and it is negative.
So, abscissa is 6, ordinate is -3
Therefore S (6, -3)
Example 2.
Find the coordinates of A, B from the following figure?
Solution:
To locate point A:
Point A is on the x-axis.
So, the y coordinate is 0.
The point is -4 units away from the origin.
So the x coordinate is -4.
Therefore, A (-4, 0).
To find point B:
It is located in the third quadrant. So both coordinates are negative.
The distance from the point to the x-axis is 7 units, the y-axis is 2 units.
Therefore, Point B (-7, -2).