Question

Calcule a distância entre os seguintes pontos: E(√3 , -1 ) e F( 0, 3 ) e assinale a alternativa correta.

√17

√13

√21

√23

√19

Answer 1

$d(E,F) = \sqrt{(x2-x1)^2 + (y2-y1)^2} \\\\ d(E,F) = \sqrt{(-1- \sqrt{3})^2 + (3-0)^2} = \\\\ d(E,F) = \sqrt{(-1- \sqrt{3})(-1- \sqrt{3}) + (3-0)^2} = \\\\ d(E,F) = \sqrt{1 + \sqrt{3} + \sqrt{3} + 3 + (3-0)^2} = \\\\ d(E,F) = \sqrt{4 + 2\sqrt{3} + 9} = \\\\ d(E,F) = \sqrt{13 + 2\sqrt{3}}$