Coordinate Geometry used in 3D

What is math

Coordinate geometry, introduced at the O-level (Ordinary Level) in mathematics education, focuses on understanding the relationships between geometric shapes and algebraic equations using a coordinate system. As a student you may find yourself plotting points along the X and Y axis or relating it to the pythagoras theorem where d = √((x2 – x1)² + (y2 – y1)²). 

In this article, let’s explore it from another angle. Have you wondered how coordinate geometry in three dimensions, often referred to as 3D coordinate geometry works? 

It extends the principles of the Cartesian coordinate system into three-dimensional space. It involves the use of a three-dimensional coordinate system to represent points, lines, planes, and other geometric objects in a three-dimensional world. Here’s an in-depth explanation of key concepts in 3D coordinate geometry!

Three-Dimensional Coordinate System

In a three-dimensional coordinate system, also known as XYZ or Cartesian coordinate system, three perpendicular axes intersect at a common point called the origin. These axes are labeled X, Y, and Z. The X-axis represents the horizontal direction, the Y-axis represents the vertical direction, and the Z-axis represents the depth or distance into or out of the plane defined by the X and Y axes.

Knowing that there is an X, Y and now a Z coordinate, it is then possible to map a specific point from the 3D perspective. For example, the point (2, 3, 4) is two units to the right along the X-axis, three units upward along the Y-axis, and four units forward along the Z-axis from the origin.

Uses in Modern Life

Putting the calculations and specifics aside, the XYZ coordinate allows us to use it for many applications in jobs that are in the design, science and navigational fields. A few examples are:

AutoCAD and 3D Modeling: In computer-aided design (CAD) software like AutoCAD, 3D coordinate geometry is used extensively to create and manipulate three-dimensional models of buildings, machinery, products, and more. Engineers, architects, and designers rely on this technology for design and prototyping.


Computer Graphics: Video games, movies, and animations rely on 3D coordinate geometry to create realistic and immersive environments. This technology is used in game development, special effects, and virtual reality applications.


GPS and Navigation Systems: The Global Positioning System (GPS) relies on 3D coordinates to pinpoint locations on the Earth’s surface. This technology is integral to modern navigation systems in cars, airplanes, and smartphones.


Geographical Information Systems (GIS): GIS software uses 3D coordinate geometry to analyze and visualize spatial data, making it valuable for urban planning, environmental monitoring, and disaster management.


Physics and Engineering: In fields like physics and engineering, 3D coordinate geometry is used to analyze the motion of objects, design structures, and model complex physical systems.


Robotics: Robotics applications often involve 3D coordinate geometry for precise movement and positioning of robotic arms, drones, and autonomous vehicles.

Can I do it?

Most importantly, even though we see the potential of doing well in coordinate geometry. It is often a question of can I do it? Can I score well in this chapter as well as in mathematics? 


Most certainly. The basics of coordinate geometry is rooted in the secondary school syllabus. For example, knowing the coordinate geometry formula is a good place to start!


If you are currently attending tuition lessons at Musclemath or have other form of support, make sure to ask your tutors about geometry questions. They can guide you through past exam papers, teach you time management strategies, and help you understand the types of questions that are commonly asked in O level exams

Here is the list of coordinate geometry formulas: 

Coordinate Geometry Formula Muscle Math

Coordinate Geometry Formula Muscle Math

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