Question

ajutor la mate ex 2 c

Answer 1

AB:(x-xA)/(xB-xA)=(y-yA)/(yB-yA)<=>AB:(x+1)/(-3+1)=(y-3)/(1-3)<=>AB:-2y+6=-2x-2<=>AB:-2y+2x+8=0 |:2=>AB:-y+x+4=0

AC:(x-xA)/(xC-xA)=(y-yA)/(yC-yA)<=>AC:(x+1)/(4+1)=(y-3)/(6-3)<=>AC:3x+3=5y-15<=>AC:-5y+3x+18=0

fie AM mediana , M∈[BC]

xM=(xC+xB)/2=(4-3)/2=1/2

yM=(yC+yB)/2=(6+1)/2=7/2

M(1/2;7/2)

AM:(x-xA)/(xM-xA)=(y-yA)/(yM-yA)<=>AM:(x+1)/(1/2+1)=(y-3)/(7/2-3)<=>AM:(x+1)/3/2=(y-3)/1/2<=>AM:x/2+1/2=3y/2-9/2<=>AM:-3y/2+x/2+5=0 |*2=>AM:-3y+x+10=0

O(0;0)

A_OAB=(|xA*yO-xA*yB+xB*yA-xB*yO+xO*yB-xO*yA)|/2=(|0+1-9-0+0-0+0|)/2=|-8|/2=8/2=4

A_OAC=(|xA*yO-xA*yC+xC*yA-xC*yO+xO*yC-xO*yA)|/2=(|0+6+12-0+0-0+0|)/2=18/2=9

√(A_OAB/A_OAC)=√(4/9)=2/3