Every location on this globe has coordinates that make it simple for us to find it on a map. Our planet’s coordinate system is made up of fictitious lines known as latitudes and longitudes. The beginning points of this coordinate system are zero degrees of “Greenwich Longitude” and zero degrees of “Equator Latitude.” We have the coordinate axes with the horizontal x-axis and the vertical y-axis, which are similar to placing the point on a piece of paper or a plane.
The study of geometric figures using coordinate axes is known as coordinate geometry. Figures like circles, ellipses, polygons, and straight lines can be drawn and scaled in the coordinate axes with ease. Additional coordinate geometry facilitates algebraic operations and the study of algebra.
In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics. In order to get a basic concept of coordinate geometry, we’ll try to learn about the coordinate plane and a point’s coordinates here.
In order to make it simple to locate the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axes of the coordinate plane. The origin is the place where these coordinate axes connect, and they divide the plane into four quadrants (0, 0).
Additionally, any point in the coordinate plane is denoted by the coordinates (x, y), where x represents the point’s position in relation to the x-axis and y represents its position in relation to the y-axis.
ThThe first quadrant’s point (x, y) is plotted with reference to the positive x-axis and the positive y-axis because it has both positive values.
With reference to the negative x-axis and positive y-axis, the point (-x, y) in the second quadrant is drawn.
Plotting is done with reference to the negative x-axis and negative y-axis for the point depicted in the third quadrant (-x, -y).
Plotting is done using the positive x-axis and the negative y-axis to depict the point in the fourth quadrant (x, -y).e characteristics of the point in the coordinate plane’s four quadrants are as follows:
The origin O is the location where the x- and y-axes intersect, and its coordinates are (0, 0).
The positive x-axis is to the right of the origin O, while the negative x-axis is to the left of the origin O. Additionally, the positive and negative y-axes are located above and below the origin O, respectively.
Application of Coordinate Geometry:
Here are a few examples of coordinate geometry in use.
- It is used to determine the separation between two places
- It is employed to determine the m:n ratios dividing line ratio
- It is used to determine a line’s midpoint
- It is used to determine a triangle’s area in the Cartesian plane
In a branch of geometry known as coordinate geometry, the location of points on a plane is determined using an ordered pair of numbers also referred to as coordinates.
Application of Coordinate Geometry in real life:
It’s always preferable to understand how information benefits us in daily life. Let’s examine the chapter’s usefulness in practice.
1. Digital Age: Text or PDF files are two examples of coordinate plane utilisation. Coordinate geometry is used to write or modify the text or graphics in these files. A 2-dimensional coordinate (x, y) system is used to read any PDF file that includes text and graphics. In order to create an exact replica of the original image that was delivered to it, scanners and photocopying equipment likewise utilise coordinate geometry.
2. Location of Air Transport: Coordinate geometry is used to manage and regulate air traffic. The current location of the aeroplane is described using the flight’s coordinates. The coordinates of flight are updated in the system for every tiny shift in an aircraft’s position, regardless of how far it moves (up, down, ahead, or backward).
3. A projected map: Map Any 3D curved object can be mapped on to a flat 2D surface using the projection technique. This method can be applied, for instance, to depict the curved surface of the earth on a flat map. A unique kind of coordinate system known as a projected coordinate system is employed for these purposes. These are primarily employed to display maps on computers.
4. GPS: The Global Positioning System (GPS) is a satellite navigation system that uses space to determine a user’s location, time, and weather.
The longitude and latitude of a location are its coordinates in a GPS. The distance formula is used to calculate the separation between two GPS locations.
5. Latitude and Longitude: In order to accurately describe a position in the actual world, a coordinate system is needed. In order to assign geographic locations, a particular coordinate system known as the geographical coordinate system is used. When tracking storms in the real world, weather forecasters periodically note the storm’s exact location to see its path and attempt to anticipate its future course in part based on these observations.
Uses of Co-Ordinate Geometry:
You can use polar coordinates for mechanical systems as well as extending them into three dimensions ( spherical coordinates ). This will be very beneficial for performing field computations. Consider the fields of electricity, magnetism, and temperature. Polar coordinates simplify calculations for physicists and engineers, to put it briefly.
For the purpose of connecting algebra and geometry with the aid of line and curve graphs, coordinate geometry is necessary. Finding points on a plane is a crucial component of mathematics. It also has a number of uses in other scientific fields such dimensional geometry, calculus, and trigonometry.
Analytic geometry, commonly referred to as coordinate geometry or Cartesian geometry in classical mathematics, is the study of geometry using a coordinate system. Synthetic geometry is in contrast to this. In addition to engineering and physics, analytical geometry is employed in space research, aviation, rocketry, and spaceflight.
Map Any 3D curved object can be mapped onto a flat 2D surface using the projection technique. This method can be applied, for instance, to depict the curved surface of the earth on a flat map. A unique kind of coordinate system known as a projected coordinate system is employed for these purposes. These are primarily employed to display maps on computers.
Coordinate geometry has several uses, including helping one understand vectors, calculus, and 3D projections. It may also be used to examine curves by producing various graphs.
For a variety of reasons, coordinate geometry is a crucial method for solving mathematical puzzles. Only the most basic mathematical shapes could be investigated in the absence of coordinate geometry. We obtain a brand-new capacity to think about position just by affixing a coordinate system to the plane (or mathematical space of another dimension). To provide a link between algebra and geometry using graphs of lines and curves, coordinate geometry is required. It is a crucial area of mathematics and typically helps us locate points on a plane. Additionally, it has several applications in the areas of trigonometry, calculus, dimensional geometry, and more.