3D Coordinates
Points (x,y,z) and distance in space.
Key idea
Points (x,y,z) and distance in space.
In depth
Three perpendicular axes locate a point as (x, y, z). Distance generalises to d = √(Δx² + Δy² + Δz²). Planes and spheres have simple equations such as x² + y² + z² = r².
Worked example
Distance from (0,0,0) to (2, 3, 6): √(4 + 9 + 36) = 7.
Formula
Real-world uses
- Locating points in a building model or drone flight plan
- Plotting data in three dimensions
Common mistake
Treating the plane view as enough; the third coordinate changes the distance.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is 3D Coordinates?
Points (x,y,z) and distance in space. It is a topic at the advanced level in Geometry.
What is the formula for 3D Coordinates?
The key formula is d = √(Δx²+Δy²+Δz²).
Where is 3D Coordinates used in real life?
Real-world examples: Locating points in a building model or drone flight plan; Plotting data in three dimensions.
What should I learn before 3D Coordinates?
Make sure you are comfortable with Cross Product (3D), the previous topic in Geometry.
What is a common mistake with 3D Coordinates?
Treating the plane view as enough; the third coordinate changes the distance.
How can I practise 3D Coordinates?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after 3D Coordinates?
Move on to Lines and Planes in 3D next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.