Question

1) Os pontos A(-6,2), B(2,-1) e C(3,5) são vértices de um triângulo. Calcule o comprimento da medida dos lados AB, AC e BC.

Answer 1

Resposta:

Explicação passo a passo:

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{d_{AB} = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}}$

$\mathsf{d_{AB} = \sqrt{(2 - (-6))^2 + (-1 - 2)^2}}$

$\mathsf{d_{AB} = \sqrt{(2 + 6)^2 + (-1 - 2)^2}}$

$\mathsf{d_{AB} = \sqrt{(8)^2 + (-3)^2}}$

$\mathsf{d_{AB} = \sqrt{64 + 9}}$

$\boxed{\boxed{\mathsf{d_{AB} = \sqrt{73}}}}$

$\mathsf{d_{AC} = \sqrt{(x_C - x_A)^2 + (y_C - y_A)^2}}$

$\mathsf{d_{AC} = \sqrt{(3 - (-6))^2 + (5 - 2)^2}}$

$\mathsf{d_{AC} = \sqrt{(3 + 6)^2 + (5 - 2)^2}}$

$\mathsf{d_{AC} = \sqrt{(9)^2 + (3)^2}}$

$\mathsf{d_{AC} = \sqrt{81 + 9}}$

$\mathsf{d_{AC} = \sqrt{90}}$

$\mathsf{d_{AC} = \sqrt{3^2.10}}$

$\boxed{\boxed{\mathsf{d_{AC} = 3\sqrt{10}}}}$

$\mathsf{d_{BC} = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2}}$

$\mathsf{d_{BC} = \sqrt{(3 - 2)^2 + (5 - (-1))^2}}$

$\mathsf{d_{BC} = \sqrt{(3 - 2)^2 + (5 + 1)^2}}$

$\mathsf{d_{BC} = \sqrt{(1)^2 + (6)^2}}$

$\mathsf{d_{BC} = \sqrt{1 + 36}}$

$\boxed{\boxed{\mathsf{d_{BC} = \sqrt{37}}}}$