Question

Dados P (x,2) , A (4,5) B (2,-8) calcule x de modo que o ponto P seja eqüidistante de A e B

Answer 1

Boa tarde!

Solução!

Pontos equidistantes.

$d(P,A)=d(P,B)$


$\sqrt{(x-4)^{2}+(2-5)^{2} }= \sqrt{(x-2)^{2} +(2+8)^{2} } \\\\ \sqrt{(x-4)^{2}+(-3)^{2} }= \sqrt{(x-2)^{2} +(10)^{2} }\\\\ \sqrt{( x^{2} -8x+16)+(9) }= \sqrt{( x^{2} -4x+4) +(100)}\\\\\ x^{2} -8x+25= x^{2} -4x+104\\\\ -8x+25=-4x+104\\\\\ -8x+4x=104-25\\\\\ -4x=79 \\\\ x=-\frac{79}{4}$

Boa tarde!