3D space, volume, angles, and midpoints
Practice Flashcards
What is the 2D distance formula between (x1,y1) and (x2,y2)?
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All Flashcards in Topic 3.1
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3.1.14 cards
What is the 2D distance formula between (x1,y1) and (x2,y2)?
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Subtract coordinates first, then square.
What is the midpoint formula in 2D?
M = ((x1+x2)/2, (y1+y2)/2)
Average x-coordinates and y-coordinates separately.
When do we use the 3D distance formula?
When points have x, y, and z coordinates.
Add the z-difference squared as well.
Common IB trap with distance questions?
Mixing up subtraction order before squaring and arithmetic slips.
Squaring removes sign, but arithmetic still matters.
3.1.24 cards
Volume of a prism formula?
Volume = cross-sectional area x length
Use consistent units (e.g., cm^3).
Volume of a cylinder formula?
V = pi r^2 h
Radius must be squared, not diameter.
Surface area vs volume: key difference?
Surface area measures outside covering; volume measures inside space.
Units: area in square units, volume in cubic units.
IB context cue for surface area?
Material needed to cover an object.
Look for paint, wrapping, or tin-sheet contexts.
Topic 3.1 study notes
Full notes & explanations for 3D space, volume, angles, and midpoints
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