The complete information on finding the coordinates of a point are given on this page. So, go through the entire article to learn the points on the coordinate plane with a detailed explanation. Also, learn the basics of coordinate geometry from here. We suggest you practice the problems given at the end of this page to know how much knowledge you have gained from this topic. So, that you can know where you are lagging and overcome the difficulties from the chapter coordinate geometry.
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What do you mean by Coordinates of a Point?
The exact position of the points on the cartesian plane is known as the coordinates of the points. We know that there are two coordinates on the plane one is x-coordinate and the other is y-coordinate. These coordinates represent the exact position of the point on a coordinate plane. There are four quadrants in the coordinate plane first quadrant has both positive values, the second quadrant has a negative x-axis, positive y-axis, the third quadrant has both negative signs and the fourth quadrant has a positive x-axis and negative y-axis.
Coordinates Meaning
A coordinate is a set of values that defines the accurate location of the points on a plane. Each point in a plane is assigned with some set of numbers called coordinates of a plane. There are two coordinates in the coordinate plane the first coordinate of a point is called x-coordinate and the second coordinate of a point is called y-coordinate.
x-coordinate:
The first number in the ordered pair is known as the x-coordinate of the point. This represents the points on the x-axis. The values on the x-axis may be positive and negative. The positive values on the x-axis will be the right side of the origin and the negative values on the x-axis will be the left side of the origin.
y-coordinate:
The second number in the ordered pair is known as the y-coordinate of the two-dimensional plane. The numbers on the y-axis are both positive and negative. The positive values on the y-axis will be located on the north and the negative values on the y-axis will be located on the south part of the graph.
x-axis: The horizontal line on the coordinate plane is known as the x-axis. The positive values on the horizontal line are indicated as the x-axis and the negative values on the horizontal line are indicated as the x’-axis.
y-axis: The vertical line on the coordinate plane is known as the y-axis. The positive values on the vertical line are indicated as the y-axis and the negative values on the vertical line are indicated as the y’-axis.
How to find Coordinates of a Point?
There are some necessary steps to follow in order to find the coordinates of a point.
1. XOX’ and YOY’ are the co-ordinate axes on the graph.
2. To locate the point on the axes we need to draw a perpendicular from P on X’OX.
3. P(OT, PT) coordinate of a point is formed.
Coordinates of a Point Examples
Example 1.
To find the coordinate of point P the distance of P from the x-axis is 4 units and the distance of P from the y axis is 6 units.
Solution:
Therefore the coordinates of a point P are (4,6).
Here a = 4 locates on x coordinate
b = 6 locates on y coordinates
Example 2.
To find the coordinate of point P the distance of P from the y-axis is 7 units and the distance of P from the x-axis is 7 units.
Solution:
Therefore the coordinates of a point P are (7,7).
Here a = 7 locates on x coordinate
b = 7 locates on y coordinates
Example 3.
In the adjoining figure, XOX’ and YOY’ are the coordinate axis. Find out the coordinates of point A?
Solution:
To locate the position of point A, draw a straight line and perpendicular line from point A to the x-axis OX, y-axis OY’.
Measure the distance between the point on the x-axis and origin, a new point on the y-axis, and origin.
The value of that point on the x-axis is 3. And the value of the point on the y-axis is -5.
So, the x coordinate is 4, y coordinate is -5.
Therefore The ordered pair is A (4, -5)
Example 4.
Find the coordinates of three marks in the following figure?
Solution:
To locate the position of point A
The ordered pair A is located in the first quadrant where both coordinates are positive.
The perpendicular distance of A from the x-axis is 4 units and the y-axis is 4 units.
So, the abscissa is 4, ordinate is 4
Therefore, the coordinates of P are (4, 4).
To locate the position of point B
The ordered pair B is also located in quadrant 1.
The perpendicular of point B from the x-axis is 0.
So, the x coordinate is 0 and the point lies on the y-axis.
The distance of B from the origin on the y-axis is 3 units.
Therefore the y coordinate is 3.
The coordinates of point Q
B (0, 3)
To locate the position of point C
Point C is located on the x-axis means its y coordinate is 0.
The distance of point C from the origin is -3 units.
So the x coordinate is -3.
Thus the Coordinates of point C (0, -3).
Example 5.
To find the coordinate of point P the distance of P from the y-axis is 3 units and the distance of P from the x-axis is -8 units.
Solution:
Therefore the coordinates of a point P are (3,-8).
Here a = 3 locates on x coordinate
b = -8 locates on y coordinates.
FAQs on Coordinates of a Point
1. How many coordinates are there at a point?
The point in a two-dimensional plane has two coordinates. One is x coordinate and it is also called abscissa and the second is y coordinate and it is also called ordinate.
2. What is meant by coordinates?
In a plane, the set of values of a point are called coordinates.
3. What do you mean by the coordinates of a point?
A pair of numbers describes the position of a point in a coordinate plane by using the horizontal and vertical distances from the two reference axis they represent by (x,y) means x coordinate and y coordinate.