Question

a distancia entre os pontos A e B é 10. Sabendo que a coordenada do ponto A é (x,-1) e B é (8,7) quais são os valores possíveis para x

Answer 1

$\Large\boxed{\begin{array}{l}\sf d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\sf 10=\sqrt{(8-x)^2+(7-[-1])^2}\\\sf 10=\sqrt{(8-x)^2+(7+1)^2}\\\sf 10=\sqrt{(8-x)^2+8^2}\\\sf(\sqrt{(8-x)^2+8^2})^2=10^2\\\sf (8-x)^2+64=100\\\sf (8-x)^2=100-64\\\sf (8-x)^2=36\\\sf (8-x)=\pm\sqrt{36}\\\sf 8-x\pm6\\\sf 8-x=6\\\sf x=8-6\\\sf x=2\\\sf 8-x=-6\\\sf x=8+6\\\sf x=14\\\sf os\,poss\acute iveis\,valores\,de\,x\,s\tilde ao\,2\,ou\,14.\end{array}}$