Question

Qual a distância entre os pontos
P (1,0) e Q =(2,V8)?
​

Answer 1

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$\Large\boxed{\begin{array}{l}\sf Seja~A(x_A,y_A)~e~B(x_B,y_B)~dois~pontos~quaisquer\\\sf pertencentes~ao~plano~cartesiano.\\\sf A~dist\hat ancia~entre~esses~pontos~\acute e\\\sf d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf P(1,0)\implies x_P=1~~y_P=0\\\sf Q(2,\sqrt{8})\implies x_Q=2~~y_Q=\sqrt{8}\\\sf d_{P,Q}=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}\\\sf d_{P,Q}=\sqrt{(2-1)^2+(\sqrt{8}-0)^2}\\\sf d_{P,Q}=\sqrt{1+8}\\\sf d_{P,Q}=\sqrt{9}\\\sf d_{P,Q}=3\end{array}}$