Distance & midpoint in 3D
Practice Flashcards
Flip to reveal answers3D distance formula?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 6 Flashcards — Distance & midpoint in 3D
Sign up free to track progress and get spaced-repetition review schedules.
Question
3D distance formula?
Answer
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²] — the 2D formula plus a z-term.
Question
3D midpoint formula?
Answer
M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) — average all three coordinates.
Question
What is a space diagonal?
Answer
The line from one corner of a cuboid to the opposite corner — found with the 3D distance formula.
Question
Distance from (0,0,0) to (2,3,6)?
Answer
√(4+9+36) = √49 = 7.
Question
Given the 3D midpoint M and one end A, find the other end B?
Answer
B = 2M − A (double the midpoint, subtract the known end), coordinate by coordinate.
Question
Most common 3D-distance error?
Answer
Adding the gaps before squaring: √(6+4+3) instead of √(36+16+9). Square each gap first.
Read the notes
Full study notes for Distance & midpoint in 3D
Topic 3.1 hub
3D space, volume, angles, and midpoints
More from Topic 3.1
All flashcards in this topic
Math AI SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free