Question

Geometria Analítica

Sabe-se que o ponto P pertence ao eixo das ordenadas e esta equidistante dos pontos A (-3, 4) e B ( 3, -2) . Calcular a abscissa do ponto P.

Answer 1

Boa tarde Wesley!

Solução!

$P(x,0)\\\\\ A(-3,4)\\\\\ B(3,-2)$

$d(A,P)=d(B,P)\\\\\\\ \sqrt{(x+3)^{2}+(0-4)^{2}}=\sqrt{(x-3)^{2}+(0+2)^{2}}\\\\\ \sqrt{ x^{2} +6x+9+16}=\sqrt{ x^{2} -6x+9 +4}\\\\\ x^{2} +6x+9+16= x^{2} -6x+9 +4\\\\\\\\\ x^{2} - x^{2} +6x+6x=-9-16+4+9\\\\\\\\\ 12x=-25+13\\\\\ 12x=-12\\\\\\ x= -\dfrac{12}{12}\\\\\\\ x= -1$

$\boxed{Resposta:x=-1}$

Boa tarde!
Bons estudos!