Definition
The orthogonal projection of M onto line D is the foot of the perpendicular from M to D.
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Lesson overview
This lesson brings together the PDF, study notes and chapter flow so you can revise Projection without losing the thread.
Definition
The orthogonal projection of M onto line D is the foot of the perpendicular from M to D.
Minimal property
The projection H is the closest point on D to M: MH ≤ MP for all P ∈ D.
Perpendicular bisector of [AB]
Set of points equidistant from A and B: MA = MB. Passes through midpoint of AB, perpendicular to AB.
Angle bisector
Ray that bisects the angle into two equal parts. Set of points equidistant from both sides.
Problem-solving method
Identify data, set formulas, solve step by step, then verify sign, unit, and coherence.
Common mistakes
Forgetting domain constraints, mixing equality/equivalence, and losing solutions during transformations.