M (3,0)
N (1,2)
P (7,4)
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MN = [tex]\displaystyle{\sqrt{(1-3)^{2} + (2-0)^{2}} }[/tex]
MN = [tex]\displaystyle{\sqrt{(-2)^{2} + 2^{2}} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}}[/tex]
NP = [tex]\displaystyle{\sqrt{(7-1)^{2} + (4-2)^{2}} }[/tex]
NP = [tex]\displaystyle{\sqrt{6^{2} + 2^{2}}= \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10} }[/tex]
MP = [tex]\displaystyle{\sqrt{(7-3)^{2} + (4-0)^{2}} }[/tex]
MP = [tex]\displaystyle{\sqrt{4^{2} + 4^{2}} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2}}[/tex]
MP² = 32
MN² = 8
NP² = 40
MP² + MN² = NP² ⇒ (conform reciprocii teoremei lui Pitagora) ⇒ ΔMNP dreptunghic
