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How to Find the Coordinates of a Point

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Last updated date: 04th Mar 2024
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Coordinate Points

Coordinates are the two numbers (Cartesian coordinates) or a letter and that point to a specific place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes usually represented as x and y axis. The horizontal and vertical distances from the two reference axes are used to describe the position of a point on a coordinate plane.


In the simplest form, there is also formula for coordinates \[y = mx + c\]


Plain Graph Along With four Quadrants


Plain Graph Along With four Quadrants 


This is quite simple right? we have got to know about coordinates, so now, let’s see about coordinates of points.


How to Find Coordinates of a Point?

  • Go to the coordinate graph with the lines X'OX (in x-axis), Y'OY (in y-axis).

  • Identify which quadrant of the graph contains an ordered pair or a point.

  • Measure the distance between the point and the x-axis.

  • Similarly, to obtain the coordinate value, measure the point's distance from the y-axis.

  • There, you will be getting the coordinates of the point.


            Not confusing, but let’s see examples which give a clear idea.


Example 1

In the below given figure, XOX’ and YOY’ are the coordinate axes. Find out the coordinates of point C?


Points Marked On a Graph

            

Points Marked On a Graph 


Solution :

  • Draw straight and perpendicular lines from point C to the x-axis OX and y-axis OY' to identify its position.

  • Calculate the distance between the newly obtained point on the x-axis, the origin, and the newly obtained point on the y-axis.

  • That location on the x-axis has a value of 2. And the y-axis point has a value of -7.

  • As a result, the x coordinate is 2 and the y coordinate is -7.

  • The point is in the fourth quadrant since the coordinate is positive and the ordinate is negative.

  • ∴ C is the ordered pair (2, -7).


How to Find Coordinates in Maths?

 A series of data that shows an exact position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down.


How to Write Coordinates of A Point?

Coordinates are written as (x, y), which means the x axis point comes first, followed by the y axis point. Some other way may be taught to remember this by saying "along the corridor, up the stairs," which means to follow the x axis first and then the y.


Conclusion 

This topic seems to be of utmost importance at the stage when a student's further study depends  on mathematics in algebra.  A coordinate framework is necessary for defining the exact location of a place in the actual world. To assign geographic locations, a special coordinate system known as the geographical coordinate system is utilised and Coordinates are integers that specify the location of a point or form in a given space (a map or a graph).


Solved Examples


1: On the Coordinate plane, write the coordinates of points A,B,C,D,E, and F.


Coordinates Marked In All Quadrants


Coordinates Marked In All Quadrants


Solution :   The provided points' coordinates are: A=(-2,1), B=(3,4), C=(1,-3), D=(-4,-2), E=(0,3), and F= (4,0).


2: On the coordinate plane, write the coordinates of points A, B, C, and D.


Distance Of Different Points On Graph


Distance Of Different Points On Graph


Solution : The distance between point A and the x axis is one unit, whereas the distance between point A and the y axis is two units. As a result, the coordinates of point A can be represented as A (-2, 1).

(ii) Regarding point B, the point is now 4 units away from the x axis and 3 units away from the y axis. As a result, the coordinates of point B can be expressed as B (3, 4).

(iii) For point C, we can see that it is in the fourth quadrant; thus, the coordinates of point C can be expressed as C (1, -3).

(iv) For point D, we can see that it is in the third quadrant. As a result, the coordinates of the D is D (-4, -2).


3: The point (12,5) is 12 units long and 5 units up


Point (12,5) Marked On Graph


Point (12,5) Marked On Graph


FAQs on How to Find the Coordinates of a Point

1. How many quadrants are there, what are they?

There are 4 quadrants. A point's coordinates in each quadrant are as follows: 

First quadrant: (+, +)

Second quadrant: (-, +)

Third quadrant: (-, -)

Fourth quadrant: (+, -)

In this case, + represents a positive real number while - represents a negative real number.

2. Find the x and y coordinates of the middle of the line connecting the points (5, -3). (1, 7).

The provided points are (5, -3) and \[({x_2},{y_2})\] respectively (1, 7).

M.P = \[\dfrac{{({x_1} + {x_2})}}{2},\dfrac{{({y_1} + {y_2})}}{2}\] is the midpoint of the line connecting these locations.

M.P = \[\dfrac{{(5 + 1)}}{2},\dfrac{{( - 3 + 7)}}{2}\]

M.P = \[\dfrac{6}{2},\dfrac{4}{2}\]

M.P = \[(3,2)\]

As a result, the x and y coordinates of the midpoint of the line connecting the two locations are (3, 2).

3. A point is located on the x-axis, 8 units away from the y-axis. What are its latitude and longitude? What are the coordinates if it is on the y-axis and -8 units away from the x-axis?

Assume the point is on the x-axis and 8 units away from the y-axis. That is, the point is in the positive x-axis direction, and its y-coordinate is 0. AAs a result, its coordinates are (8, 0).

If the point is -8 units from the x-axis on the y-axis, its x-coordinate must be 0, and the point is in the negative direction of the y-axis. 

As a result, its coordinates are (0, -8).

4. Write the coordinates of each of the given figure's points P,Q,R,S,T, and .Image coordinate marked on graph

The coordinates of the needed points are as follows.

P⟹(1,1) 

Q⟹(−3,0) 

R⟹(−2,−3)

S⟹(2,1)

T⟹(4,−2)

O⟹(0,0)

This image shows  Coordinates Of Points P,Q,R,S,T


Coordinates Of Points P,Q,R,S,T

5. Rectangle ABCD has the following coordinates: A(-5,2), B(8,2), and C(8, -4). Determine D's coordinates.

A graph can assist you solve this challenge. Please see the figure. D must have the coordinates (5,4).


This image shows Coordinates Of Points A,B,C,D On The Graph


Coordinates Of Points A,B,C,D On The Graph