Question

dados dois pontos A (1,3) e B (9,-3), a distancia de AB vale
a. 8
b. 9
c. 10
d. 11
e. 12​

Answer 1

$\large\boxed{\begin{array}{l}\sf Dados~os~pontos~A(x_A,y_A)~e~B(x_B,y_B)\\\sf a~dist\hat ancia~entre~A~e~B~\acute e~dado~por\\\sf d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf A(1,3)~~B(9,-3)\\\sf d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\sf d_{A,B}=\sqrt{(9-1)^2+(-3-3)^2}\\\sf d_{A,B}=\sqrt{8^2+(-6)^2}\\\sf d_{A,B}=\sqrt{64+36}\\\sf d_{A,B}=\sqrt{100}\\\sf d_{A,B}=10\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$

Answer 2

Oie, tudo bom?

Resposta: c) 10.

$\boxed{A(1 \: , \: 3) \: e \: B(9 \: , \: - 3) \: \: \: \: \: \: A(X _{a} \: , \: Y _{a}) \: e \: B(X_{b} \: , \: Y _{b})}$

$d = \sqrt{(X_{b} - X _{a}) {}^{2} + ( Y _{b} - Y _{a}) {}^{2} } \\ d = \sqrt{(9 - 1) {}^{2} + ( - 3 - 3) {}^{2} } \\ d = \sqrt{8 {}^{2} + ( - 6) {}^{2} } \\ d = \sqrt{64 + 36} \\ d = \sqrt{100} \\ \boxed{d = 10}$

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