A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.
Coordinates Definition
A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.
The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:
x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.
y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.
Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).
Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).
How to Find Coordinates of a Point?
Below given are the steps that are helpful to find the coordinates of a point. Go through them.
- Go to the coordinate graph having lines X’OX, Y’OY.
- Check out which quadrant of the graph has an ordered pair or a point.
- To get the abscissa, measure the distance of the point from the x-axis.
- Likewise, measure the distance of the point from the y-axis to obtain the ordinate value.
Solved Example Questions
Example 1.
In the adjoining figure, XOX’ and YOY’ are the co-ordinate axes. Find out the coordinates of point C?
Solution:
To locate the position of point C draw straight and perpendicular lines from point C to the x-axis OX, y-axis OY’.
Measure the distance between the newly obtained point on the x-axis, origin, new point on the y-axis, and origin.
The value of that point on the x-axis is 2. And the value of the point on the y-axis is -7.
So, the x coordinate is 2, y coordinate is -7.
As the abscissa is positive and ordinate is negative, the point lies in the fourth quadrant.
∴ The ordered pair is C (2, -7)
Example 2.
Find the coordinates of three marked in the following figure?
Solution:
To locate the position of point P:
The ordered pair P is located in the first quadrant where both coordinates are positive.
The perpendicular distance of P from the x-axis is 5 units and the y-axis is 4 units.
So, the abscissa is 5, ordinate is 4
Therefore, the coordinates of P are (5, 4).
To locate the position of point Q:
The ordered pair Q is also located in quadrant 1.
The perpendicular of the point Q from the x-axis is 0.
So, the x coordinate is 0 and the point lies on the y-axis.
the distance of Q from the origin on the y-axis is 3 units.
So, y coordinate is 3.
The coordinates of point Q (0, 3)
To locate the position of point R:
The point R is located on the x-axis means its y coordinate is 0.
The distance of the point Q from the origin is -2 units.
So the x coordinate is -2.
The Coordinates of point R (0, -2).
Frequently Asked Questions on Coordinates of a Point
1. How many coordinates are there in a point?
For every point on a two-dimensional plane, we have two coordinates. One is x coordinate or abscissa and the second is y coordinate or ordinate.
2. What is meant by coordinates?
In a cartesian plane, the values of a point are called coordinates.