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Tussentijdse toetsen

2006-04-??

  1. Geef een basis voor de richting van de volgende affiene deelruimte van :



  2. Zij S een niet-lege deelverzameling van . Toon aan: S is een affiene deelruimte van als en slechts als voor elk tweetal punten p, q van S de verbindingsrechte pq tot S behoort.
  3. Zij b, c twee vaste punten in en L een vaste rechte die bc snijdt in p. Toon aan dat de zwaartepunten van de driehoeken abc, waarbij a varieert op L \ {p}, steeds tot een vaste rechte behoren. Doe dit
    • analytisch;
    • synthetisch.
    (Voor het synthetisch bewijs mag je alle eigenschappen uit de cursus en de oefenzittingen gebruiken, maar zeg er wel bij welke eigenschap je gebruikt.)