Question

Fie punctele M(1;2) N(5;1) P(1;1). Aratati ca triunghiul MNP este dreptunghic!!!!
Va rogg sa ma ajutati cat mai repede posibil. ACEASTA LECTIE E LA ALGEBRA.

Answer 1

M(1;2) N(5;1) P(1;1)

Demonstram ca MN² = MP²+ NP²

$MN = \sqrt{(5-1)^2+(1-2)^2} = \sqrt{16+1} = \sqrt{17} \\ \\ MP = \sqrt{(1-1)^2+(1-2)^2} = 1 \\ \\ NP= \sqrt{(1-5)^2+(1-1)^2} = \sqrt{4^2} = 4 \\ \\ \\ \\ MN^2 = MP^2+NP^2 \Rightarrow \sqrt{17}^2= 1^2+4^2 \Rightarrow 17 = 1 + 16 \Rightarrow \\ \Rightarrow 17 = 17 (Adevarat ) \Rightarrow \triangle_{MNP}\rightarrow dreptunghic$