Question

calcular a distância entre os pontos (1,1)e b (4,4)

Answer 1

A distancia entre dois pontos é dada por:

$Distancia_{A,B}~=~\sqrt{\left(x_A-x_B\right)^2~+~\left(y_A-y_B\right)^2}$

Substituindo as coordenadas fornecidas pelo enunciado:

$Distancia_{A,B}~=~\sqrt{\left(1-4\right)^2~+~\left(1-4\right)^2}\\\\\\Distancia_{A,B}~=~\sqrt{\left(-3\right)^2~+~\left(-3\right)^2}\\\\\\Distancia_{A,B}~=~\sqrt{9~+~9}\\\\\\Distancia_{A,B}~=~\sqrt{18}\\\\\\Distancia_{A,B}~=~\sqrt{2\cdot3^2}\\\\\\\boxed{Distancia_{A,B}~=~3\sqrt{2}}$

Answer 2

$\large \boxed{ \begin{array}{l} \sf{d_{AB} = \sqrt{(x_A - x_B) {}^{2} + (y_A - y_B) {}^{2} } } \\ \\ \sf{d_{AB} = \sqrt{(1 - 4) {}^{2} + (1 - 4) {}^{2} } } \\ \\ \sf{d_{AB} = \sqrt{( - 3) {}^{2} + ( - 3) {}^{2} } } \\ \\ \sf{d_{AB} = \sqrt{9 + 9} } \\ \\ \sf{d_{AB} = \sqrt{18} } \\ \\ \boxed{ \boxed{ \sf{d_{AB} = 3\sqrt{2} }}}\end{array}}$