Question

Adistancia do ponto A(a, 1) ao ponto B (0,2) e igual a 3 calcule o valor da abscisso a

Answer 1

Pontos:   $A(a,\,1)~\text{ e }~B(0,\,2).$


Fórmula da distância entre dois pontos:

$d_{A,\,B}=3\\\\ \sqrt{(x_{_B}-x_{_A})^2+(y_{_B}-y_{_A})^2}=3\\\\ \sqrt{(0-a)^2+(2-1)^2}=3\\\\ \sqrt{(-a)^2+(1)^2}=3\\\\ \sqrt{a^2+1}=3\\\\ \big(\sqrt{a^2+1}\big)^2=3^2$

$a^2+1=3^2\\\\ a^2+1=9\\\\ a^2=9-1\\\\ a^2=8\\\\ a=\pm \sqrt{8}\\\\ a=\pm \sqrt{2^3}\\\\ a=\pm \sqrt{2^2\cdot 2}\\\\ a=\pm 2\sqrt{2}\\\\ \boxed{\begin{array}{c}a=-2\sqrt{2}~~\text{ ou }~~a=2\sqrt{2} \end{array}}$


Dúvidas? Comente.


Bons estudos! :-)