Q: Extend f(x,0) = x from x-axis to ℝ² dominated by ‖·‖₂. Subspace M = {(x,0)}. f(x,0) = x: |f| ≤ ‖(x,0)‖₂ ✓. Hahn-Banach: extends to F on ℝ², |F| ≤ ‖·‖₂. F(x,y) = x works: |x| ≤ √(x²+y²) ✓! (Norm-preserving extension!) Geometric: separate point from convex set!