Question

Um seguimento PQ tem o comprimento de ²√26. Sendo P(-1,2) e Q(4,y), calcule y.

Answer 1

${(x_{Q}-x_{P})}^{2}={(4-[-1])}^{2}=25$

${(y_{Q}-y_{P})}^{2}={(y-2)}^{2}$

$d_{P,Q}=\sqrt{{(x_{Q}-x_{P})}^{2}+{(y_{Q}-y_{P})}^{2}}$

$\mathsf{\sqrt{26}=\sqrt{25+{(y-2)}^{2}}}$

$\mathsf{{(y-2)}^{2}=26-25}\\\mathsf{{(y-2)}^{2}=1}\\\mathsf{y-2=\pm\sqrt{1}}$

$\mathsf{y-2=1}\\\mathsf{y=2+1=3}\\\mathsf{y-2=-1}\\\mathsf{y=2-1=1}$

$\boxed{\boxed{\mathsf{y=3\,ou\,y=1}}}$