What Are Coordinates Of A Point Definition Formula And Solved Examples
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
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 In The Cartesian Plane
1. What are the coordinates of a point in mathematics?
The coordinates of a point are an ordered pair of numbers that show its exact position on the coordinate plane. In a 2D Cartesian plane, coordinates are written as (x, y), where:
- x-coordinate represents the horizontal position (along the x-axis).
- y-coordinate represents the vertical position (along the y-axis).
2. How do you find the coordinates of a point on a graph?
To find the coordinates of a point on a graph, read the horizontal value first and the vertical value second. Follow these steps:
- Move horizontally from the origin to the point to find the x-coordinate.
- Move vertically to find the y-coordinate.
- Write the ordered pair as (x, y).
3. What is the formula for the distance between two coordinates?
The distance formula between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²]. This formula is derived from the Pythagorean theorem.
- Subtract the x-coordinates.
- Subtract the y-coordinates.
- Square both differences and add them.
- Take the square root.
4. What is the midpoint of two coordinates?
The midpoint of two coordinates is the point exactly halfway between them, calculated using ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Add the x-coordinates and divide by 2.
- Add the y-coordinates and divide by 2.
5. What is the origin in coordinates?
The origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0). It represents zero horizontal and zero vertical movement. All positions on the coordinate plane are measured relative to the origin.
6. What is the difference between x-coordinate and y-coordinate?
The x-coordinate shows horizontal position, while the y-coordinate shows vertical position.
- x-coordinate: Movement left (negative) or right (positive) along the x-axis.
- y-coordinate: Movement down (negative) or up (positive) along the y-axis.
7. How do you plot coordinates on a Cartesian plane?
To plot coordinates on a Cartesian plane, start at the origin and move according to the ordered pair (x, y).
- Move horizontally to the x-value.
- Move vertically to the y-value.
- Mark the point where both movements meet.
8. In which quadrant does a point lie?
A point’s quadrant depends on the signs of its coordinates.
- Quadrant I: (+, +)
- Quadrant II: (−, +)
- Quadrant III: (−, −)
- Quadrant IV: (+, −)
9. Can coordinates have negative values?
Yes, coordinates can have negative values depending on their position relative to the origin.
- Negative x-values lie to the left of the origin.
- Negative y-values lie below the origin.
10. What are coordinates used for in real life?
Coordinates are used to precisely locate positions in mathematics, maps, navigation, and technology. Common applications include:
- GPS systems using latitude and longitude.
- Graphing equations in algebra.
- Computer graphics and game design.
- Engineering and architecture measurements.
