Question

Im reperul cartezian xOy se considera punctele A(1,1) , B(4,1) , C(4,4).Aratati ca AB=BC.

Answer 1

Aplicam formula distantei dintre doua puncte.

$AB = \sqrt{(xA-xB)^{2} + (yA-yB)^{2} } \\ \\ AB = \sqrt{(1-4)^{2} + (1-1)^{2} } \\ \\ AB = \sqrt{(-3)^{2}+0^{2} } \\ \\ AB = \sqrt{9+0} \\ \\ AB = \sqrt{9} \\ \\ AB = 3$

$BC = \sqrt{(xB-xC)^{2} + (yB-yC)^{2} } \\ \\ BC = \sqrt{(4-4)^{2}+ (1-4)^{2} } \\ \\ BC = \sqrt{0^{2} + (-3)^{2} } \\ \\ BC = \sqrt{0+9} \\ \\ BC = \sqrt{9} \\ \\ BC = 3$

Din cele doua calcule ⇒ AB = BC = 3.

Sper ca te-am ajutat.