Question

Num plano Cartesiano, encontre a distância entre os pontos

Coordenadas: (√2, -√2 ) e ( -√2, √2 )

Answer 1

Boa tarde!

Formula da distância!


$d(A,B)= \sqrt{(yB-yA)^{2}+(xB-xA)^{2}}\\\\\\\\ Pontos!\\\\\\\ A( \sqrt{2}, -\sqrt{2})\\\\\\ B( -\sqrt{2} , \sqrt{2})$


$d(A,B)= \sqrt{( \sqrt{2}+ \sqrt{2})^{2}+(- \sqrt{2} - \sqrt{2} )^{2}}\\\\\\\\ d(A,B)= \sqrt{( 2\sqrt{2})^{2}+(- 2\sqrt{2})^{2}}\\\\\\\\ d(A,B)= \sqrt{( 4\times2)+(4\times2)}\\\\\\\\ d(A,B)= \sqrt{8+8}\\\\\\\\ d(A,B)= \sqrt{16}\\\\\\\\ \boxed{Resp~~d(A,B)= 4}$

Boa tarde!