Question

O triângulo formado pelos pontos A( 7 , 3) B(-4, 4) e C(-4, 2) , tem o ponto médio entre B e C com coordenadas correspondentes. Logo, qual o comprimento da mediana ¯AM? *

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{M_{BC} = \left(\dfrac{x_B + x_C}{2}\:;\:\dfrac{y_B + y_C}{2}\right)}$

$\mathsf{M_{BC} = \left(\dfrac{-4 - 4}{2}\:;\:\dfrac{4 + 2}{2}\right)}$

$\mathsf{M_{BC} = \left(\dfrac{-8}{2}\:;\:\dfrac{6}{2}\right)}$

$\mathsf{M_{BC} = \left(-4\:;\:3\right)}$

$\mathsf{D_{AM} = \sqrt{(x_A - x_M)^2 + (y_A - y_M)^2}}$

$\mathsf{D_{AM} = \sqrt{(7 - (-4))^2 + (3 - 3)^2}}$

$\mathsf{D_{AM} = \sqrt{(7 + 4)^2 + (3 - 3)^2}}$

$\mathsf{D_{AM} = \sqrt{(11)^2 + (0)^2}}$

$\mathsf{D_{AM} = \sqrt{121 + 0}}$

$\mathsf{D_{AM} = \sqrt{121}}$

$\boxed{\boxed{\mathsf{D_{AM} = 11}}}$