a) M( xA+xB /2 , yA+yB /2)
M(4/2 , 10/2) ==> M(2,5)
b) Ecuatia unei drepte data de doua puncte ( determinant)
(AB): [tex]\left[\begin{array}{ccc}x&y&1\\xA&yA&1\\xB&yB&1\end{array}\right][/tex]
(AB): [tex]\left[\begin{array}{ccc}x&y&1\\1&4&1\\3&6&1\end{array}\right][/tex]
(AB): (4x+3y+6)-(12+y+6x)=4x+3y+6-12-y-6x= -2x+2y-6=0 (determinantul = 0)
2y=2x+6 | :2
y=x+3
c) AB=[tex]\sqrt{ (xB-xA)^{2}+(yB-yA)^{2} }[/tex] ==> Distanta (lungimea) dintre doua puncte
AB=[tex]\sqrt{4+4} =\sqrt{8} =2\sqrt{2}[/tex]
d) C(2,2) || AB
(g)=?
(AB): y=x+3 ==> m=1 (m=panta)
y-yC=m(x-xC) ==>Ecuatia unei drepte data de un punct si o panta
y-2=x-2 ==> y+x=0
