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All 8 Flashcards — Distance & midpoint (3D)
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Question
3D distance formula?
Answer
d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²) — Pythagoras with a z-term.
Question
3D midpoint formula?
Answer
((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) — average each coordinate.
Question
Distance vs midpoint — what's the difference?
Answer
Distance squares the gaps and roots; midpoint averages the coordinates.
Question
Does the order of points matter for distance?
Answer
No — each gap is squared, so the sign disappears.
Question
Given midpoint M and endpoint A, how do you find B?
Answer
B = 2M − A (each coordinate).
Question
Distance from origin to (2, 3, 6)?
Answer
√(4 + 9 + 36) = √49 = 7.
Question
Space diagonal of a box with edges l, w, h?
Answer
√(l² + w² + h²).
Question
How do you check a midpoint answer?
Answer
Average the two endpoints — you should recover the midpoint.
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Full study notes for Distance & midpoint (3D)
Topic 3.1 hub
3D geometry
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Math AA SL exam skills
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