Question

Fie segmentul [AB] si punctele M, N apartinand (AB) astfel incat AM/MB = 3/2 si AN/NB = 2/3. Daca P este mijlocul lui [AB] aflati AP/PM si AN/NP. URGENT!!!!! VA ROG CAT MAI DETALIAT

Answer 1

A/------/------/------/------/------/B
                 N  P M

AM/MB=3/2
scriu rapoarte egale
AM/AM+MB=AM/AB=3/2+3=3/5
AM=3k, AB=5k

AN/NB=2/3
AN/AN+NB=AN/AB=2/2+3=2/5 
⇒AN=2k, AB=5k


P mijlocul lui AB
AP=5k/2
MN=AM-AN=3k-2k=k
PM=AM-AP=3k-5/2*k=k/2
AP/PM=5k/2:k/2=5k/2*2/k=5

NP=AP-AN=5k/2-2k=k/2
AN/NP=2k:k/2=2k*2/k=4