How to Find and Plot Coordinates in Maths
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
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
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
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
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
FAQs on Coordinates of a Point: Step-by-Step Guide for Students
1. What are the coordinates of a point and how are they written?
The coordinates of a point are a pair of numbers that define its exact location on a Cartesian plane. They are always written as an ordered pair (x, y). The first number, 'x', is the x-coordinate (abscissa), and the second number, 'y', is the y-coordinate (ordinate). For example, the point (3, 4) is located 3 units along the x-axis and 4 units along the y-axis.
2. How do you find the coordinates of any given point on a graph?
To find the coordinates of a point on a graph, follow these steps:
- Find the x-coordinate (abscissa): Draw a perpendicular line from the point to the x-axis. The value where this line meets the x-axis is the x-coordinate. It represents the horizontal distance from the y-axis.
- Find the y-coordinate (ordinate): Draw a perpendicular line from the point to the y-axis. The value where this line meets the y-axis is the y-coordinate. It represents the vertical distance from the x-axis.
- Write the ordered pair: Combine these two values as (x, y).
3. What is the difference between an abscissa and an ordinate?
The terms abscissa and ordinate refer to the two components of a coordinate pair (x, y):
- The abscissa is the x-coordinate. It specifies the point's horizontal distance from the y-axis.
- The ordinate is the y-coordinate. It specifies the point's vertical distance from the x-axis.
In the coordinate (5, -2), the abscissa is 5 and the ordinate is -2.
4. What are the four quadrants, and what are the signs of coordinates in each?
The x-axis and y-axis divide the Cartesian plane into four regions called quadrants. The signs of the coordinates (x, y) are unique in each quadrant:
- Quadrant I: Both x and y are positive (+, +).
- Quadrant II: x is negative, and y is positive (-, +).
- Quadrant III: Both x and y are negative (-, -).
- Quadrant IV: x is positive, and y is negative (+, -).
5. What are the coordinates of a point that lies on the x-axis or the y-axis?
The location of a point on an axis is a special case:
- Any point on the x-axis has a y-coordinate of 0. Its coordinates will be in the form (x, 0).
- Any point on the y-axis has an x-coordinate of 0. Its coordinates will be in the form (0, y).
The point where both axes intersect is the origin, with coordinates (0, 0).
6. Why is the order of coordinates important? Is the point (2, 5) the same as (5, 2)?
The order of coordinates is crucial because it specifies a unique location. The point (2, 5) is not the same as (5, 2).
- Point (2, 5): You move 2 units to the right on the x-axis and then 5 units up on the y-axis.
- Point (5, 2): You move 5 units to the right on the x-axis and then 2 units up on the y-axis.
These are two completely different points on the plane. This is why coordinates are called an 'ordered pair'—the order matters.
7. How does the Cartesian coordinate system help describe a location precisely?
The Cartesian system provides a precise framework for locating points by using two fixed perpendicular lines (axes) as a reference. Instead of vague descriptions like "up and to the right," it gives an exact address. For example, (4, 3) tells us to move exactly 4 units horizontally and 3 units vertically from a universal starting point (the origin). This numerical precision is fundamental in fields like mapping, engineering, and computer graphics.
8. What are the coordinates of the origin and why is it considered a special point?
The coordinates of the origin are (0, 0). It is a special point because it is the intersection of the x-axis and the y-axis. The origin serves as the universal reference point for all other coordinates on the Cartesian plane. Every coordinate pair (x, y) represents a distance and direction measured starting from the origin.
