Question

determinar a d(A,B) de modo que: A(a ; b) e B(a/2 ; b/4) sendo que: a + b = 6 e a - b = 4.

Answer 1

 Resolvendo o sistema,

$\begin{cases}a+b=6\\a-b=4\end{cases}\\---------\\a+b+a-b=6+4\\2a=10\\\boxed{a=5}$
 
 Calculando b,

$a+b=6\\5+b=6\\\boxed{b=1}$
 
 Portanto, A = (5, 1) e B = (5/2, 1/4).
 
 Isto posto,

$d_{A,B}=\sqrt{(\frac{5}{2}-5)^2+(\frac{1}{4}-1)^2}\\\\d_{A,B}=\sqrt{(\frac{-5}{2})^2+(\frac{-3}{4})^2}\\\\d_{A,B}=\sqrt{\frac{25}{4}+\frac{9}{16}}\\\\\boxed{\boxed{d_{A,B}=\frac{\sqrt{109}}{4}}}$