A(0,a)B(-1,2)c(4,5)
Calculez lungimile laturilor aplicand formula:
[tex]AB = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex] , , unde A(x1,y1) si B(x2,y2)
[tex]AB = \sqrt{ (-1-0)^{2} + (2-a)^{2} } = \sqrt{ a^{2} -4a+5 } [/tex]
[tex]BC = \sqrt{ (4+1)^{2} + (5-2)^{2} } = \sqrt{34} [/tex]
[tex]AC = \sqrt{ (4-0)^{2} + (5-a)^{2} } = \sqrt{ a^{2} -10a+41 } [/tex]
Conditie ca triunghiul ABC sa fie dreptunghic:
[tex] BC^{2} = AB^{2} + AC^{2} [/tex]
[tex]34 = | a^{2} -4a+5| + | a^{2} -10a+41|[/tex]
[tex]34 = 2a^{2} -14a+46[/tex]
[tex] 2a^{2} -14a+12 = 0 [/tex] (impart ecuatia la 2)
[tex]a^{2} -7a+6=0[/tex]
Δ = 49 - 24
Δ = 25
a1 = (7-5):2
a1=1
a2=(7+5):2
a2=12:2
a2=6
Raspuns final : a =1 sau a=6