Question

Calcule a distância entre os pontos A e B
A=(5,-2) B=(1,1) ?

Answer 1

A distancia entre pontos é dada por:

$Distancia = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\Substituindo\;os\;pontos\;na\;formula:\\\\Distancia = \sqrt{(1-5)^2+(1-(-2))^2}\\\\Distancia = \sqrt{(-4)^2+(1+2)^2}\\\\Distancia = \sqrt{16+(3)^2}\\\\Distancia = \sqrt{16+9}\\\\Distancia = \sqrt{25}\\\\Distancia = 5$

Answer 2

$\large \boxed{ \begin{array}{l} \sf{d_{AB} = \sqrt{(x_A - x_B) {}^{2} + (y_A - y_B) {}^{2} } } \\ \\ \sf{d_{AB} = \sqrt{(5 - 1) {}^{2} + (( - 2) - 1) {}^{2} } } \\ \\ \sf{d_{AB} = \sqrt{4 {}^{2} + ( - 3) { }^{2} } } \\ \\ \sf{d_{AB} = \sqrt{16 + 9} } \\ \\ \sf{ d_{AB} = \sqrt{25} } \\ \\ \boxed{ \sf{d_{AB} = 5}}\end{array}}$