Question

Qual a distância entre os pontos C e D cujas coordenadas são C(2,5) e D (10,15)?

a)100,81
b)64,81
c)60,81
d)30,81
e)12,81​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{D_{CD} = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2}}}$

$\mathsf{D_{CD} = \sqrt{(10 - 2)^2 + (15 - 5)^2}}}$

$\mathsf{D_{CD} = \sqrt{(8)^2 + (10)^2}}}$

$\mathsf{D_{CD} = \sqrt{64 + 100}}}$

$\mathsf{D_{CD} = \sqrt{164}}}$

$\boxed{\boxed{\mathsf{D_{CD} = 12,81}}}}\leftarrow\textsf{letra E}$

Answer 2

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

$\boxed{\begin{array}{l}\sf C(2,5)~D(10,15)\\\sf d_{C,D}=\sqrt{(10-2)^2+(15-5)^2}\\\sf d_{C,D}=\sqrt{64+100}\\\sf d_{C,D}=\sqrt{164}\\\begin{array}{c|l}\sf164&\sf2\\\sf82&\sf2\\\sf41&\sf41\\\sf1\end{array}\\\sf 164=2^2\cdot41\\\sf\sqrt{164}=\sqrt{2^2\cdot41}=2\sqrt{41}\\\sf d_{C,D}=2\sqrt{41}\approx12,81\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~e}}}}\end{array}}$