Question

Qual é o valor de “m” para que a distância entre os pontos A (- 1, 2, 3) e B (1, - 1, m) seja 7 ? GEOMETRIA ANALITICA

Answer 1

Resposta:

m=9 ou m=-3

Explicação passo-a-passo:

distância entre dois pontos

$D_A_B=\sqrt{(x_B-x_A)^{2}+(y_B-y_A)^{2}+(z_B-z_A)^{2}}\\\\\\Substituindo\\\\\sqrt{(1-(-1))^{2}+(-1-2)^{2}+(m-3)^{2}}=7\\\\\\\sqrt{(1+1)^{2}+(-3)^{2}+m^{2}-6m+9}=7\\\\\\\sqrt{2^{2}+9+m^{2}-6m+9}=7\\\\\\\sqrt{4+m^{2}-6m+18}=7\\\\\\\sqrt{m^{2}-6m+22}=7\\\\\\(\sqrt{m^{2}-6m+22})^{2} =7^{2}\\\\m^{2}-6m+22=49\\\\m^{2}-6m+22-49=0\\\\m^{2}-6m-27=0$

$\Delta=(-6)^{2}-4.1.(-27)=36+108=144\\\\m=\dfrac{-(-6)\pm\sqrt{144}}{2.1}\\\\m=\dfrac{6\pm12}{2}\\\\m'=\dfrac{6+12}{2}=\dfrac{18}{2}=9\\ \\ou\\\\m"=\dfrac{6-12}{2}=\dfrac{-6}{2}=-3$