Question

Calcule a distância do ponto A(1,1) ao ponto B(6,13)

Answer 1

Podemos resolver por teorema de pitágoras:

$dist\^ancia^2=(x_1-x_0)^2+(y_1-y_0)^2\\\\ dist\^ancia^2=(6-1)^2+(13-1)^2\\\\ dist\^ancia^2=5^2+12^2\\\\ dist\^ancia^2=25+144\\\\ dist\^ancia^2=169\\\\ dist\^ancia = \pm \sqrt{169}\\\\ dist\^ancia = \pm 13\ (\ utilizaremos\ apenas\ a\ parte\ positiva,\\ ~~~~~~~~~~~~~~~~~~~~~~~~~\ por\ se\ tratar\ de\ dist\^ancia\ )\\\\ \boxed{dist\^ancia = 13\ un.}$



Bons estudos!

Answer 2

$\large \boxed { \begin{array}{l} \rm \: d = \sqrt{(x_a - x_b)^2 + (y_a - y_b)^2 } \\ \rm \: d = \sqrt{(1 - 6) {}^{2} +( 1 - 13 ) {}^{2} } \\ \rm \: d = \sqrt{( - 5) {}^{2} + (- 12 ) {}^{2} } \\ \rm \: d = \sqrt{25 + 144} \\ \rm \: d = \sqrt{169} \\ \boxed{\rm d = 13}\end{array}}$