Question

(UFSC) Dados os pontos A(-1,-1), B(5, -7) e C(x,2), determine x sabendo que o ponto C é equidistante dos pontos A e B. a) 8 b) 6 c) 15 d) 12 e) 7

Answer 1

Resposta:

Explicação passo-a-passo:

Olá

$AC\\D=\sqrt{(\Delta X)^{2} +(\Delta Y)^{2} }\\\\D=\sqrt{(-1-X)^{2} +(-1-2)^{2} }\\\\D=\sqrt{(1+2X+X^{2}+ (-3)^{2} }\\\\D=\sqrt{(+2X+X^{2}+ 10 }\\\\\\BC\\D=\sqrt{(5-X)^{2} +(-7-2)^{2} }\\\\D=\sqrt{25-10X+X^{2} +(-9)^{2} }\\\\D=\sqrt{25-10X+X^{2} +81 }\\\\D=\sqrt{106-10X+X^{2} }\\\\IGUALANDO:\\\\\sqrt{(+2X+X^{2}+ 10 }=\sqrt{106-10X+X^{2} }\\\\2X+X^{2}+ 10 =106-10X+X^{2}\\\\2X+ 10 =106-10X\\\\12X+ 10 =106\\\\12X=106-10\\\\12X=96\\\\X=\frac{96}{12}$

Portanto temos que:

$\checkmark\boxed{\boxed{X\Rightarrow\boxed8}}$