Question

Apresente a equação da reta mediatriz do segmento de reta que liga os pontos A(14, - 5) e B(8, 17)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{A(14,-5)\:\:\:\:\:B(8,17)}$

$\mathsf{M\left(\dfrac{x_A + x_B}{2};\:\dfrac{y_A + y_B}{2}\right)}$

$\mathsf{M\left(\dfrac{14 + 8}{2};\:\dfrac{-5 + 17}{2}\right)}$

$\mathsf{M\left(\dfrac{22}{2};\:\dfrac{12}{2}\right)}$

$\boxed{\boxed{\mathsf{M(11;\:6)}}}\leftarrow\textsf{ponto m{\'e}dio}$

$\mathsf{m = \dfrac{\Delta_Y}{\Delta_X} = \dfrac{y_B - y_A}{x_B - x_A} = \dfrac{17 -(-5)}{8 - 14} = \dfrac{17 + 5}{8 - 14} = -\dfrac{22}{6} = -\dfrac{11}{3}}$

$\mathsf{r \perp s \iff m_r.m_s = -1}$

$\mathsf{m.\left(-\dfrac{11}{3}\right) = -1}$

$\boxed{\boxed{\mathsf{m = \dfrac{3}{11}}}}\leftarrow\textsf{coeficiente angular}$

$\mathsf{y - y_0 = m(x - x_0)}$

$\mathsf{y - 6 = \dfrac{3}{11}(x - 11)}$

$\boxed{\boxed{\mathsf{3x - 11y + 33 = 0}}}$