Don't Drop the z-term

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Watch Out

The most common 3D mistake. Students apply the 2D distance formula and forget $z$, getting wrong answers that are always one of the distractors. Always check: is this a 3D problem? Then include $z$.

2D: Δ x^{2} + Δ y^{2} 3D: Δ x^{2} + Δ y^{2} + Δ z^{2}

The trap: dropping $\Delta z^{2}$

Count coords

2 each vs 3 each

Decides 2D vs 3D formula

Same $z$ ?

$Δ z = 0$

3D formula still works — just adds 0

Mistake

Using 2D in 3D

Always wrong when $z$ values differ