Question

calcule em cada caso a distancia os pontos a (1,3) e (9,9) B (-4, -2)e (0,7)

Answer 1

$<var>caso \ A \Longrightarrow dist\^{a}ncia(d) \ entre \ (1,3) \ e \ (9,9) \\\\ d = \sqrt{(X_{f}-X_{i})^{2}+(Y_{f}-Y_{i})^{2}} \\ d = \sqrt{(9-1)^{2}+(9-3)^{2}} \\ d = \sqrt{(8)^{2}+(6)^{2}} \\ d = \sqrt{64+36} \\ d = \sqrt{100} \\ \boxed{d = 10}</var>$

 

$<var>\dotfill</var>$

 

$<var>caso \ B \Longrightarrow dist\^{a}ncia(d) \ entre \ (-4,-2) \ e \ (0,7) \\\\ d = \sqrt{(X_{f}-X_{i})^{2}+(Y_{f}-Y_{i})^{2}} \\ d = \sqrt{(0-(-4))^{2}+(7-(-2))^{2}} \\ d = \sqrt{(0+4)^{2}+(7+2)^{2}} \\ d = \sqrt{(4)^{2}+(9)^{2}} \\ d = \sqrt{16+81} \\ \boxed{d = \sqrt{97}}</var>$

Answer 2

Para calcular a distância usamos a fórmula:

 

$<var>d = \sqrt{(X_f - X_i)^2\ +\ (Y_f - Y_i)^2}</var>$

 

Pontos : Xfinal = 9 - Xinicial = 1

Yfinal = 9 - Yinicial = 3

 

$<var>d = \sqrt{(9- 1)^2\ +\ (9 - 3)^2}</var>$

 

$<var>d = \sqrt{(64 + 36}</var>$

 

$<var>d = \sqrt{100}</var>$

 

$<var>\boxed{d=10}</var>$

 

Agora a distancia do caso B

 

$<var>d = \sqrt{(X_f - X_i)^2\ +\ (Y_f - Y_i)^2}</var>$

 

$<var>d = \sqrt{(0 - (-4))^2\ +\ (7-(-2))^2}</var>$

 

$<var>d = \sqrt{(4)^2\ +\ (9)^2}</var>$

 

$<var>d = \sqrt{16 + 81}</var>$

 

$<var>d = \sqrt{97}</var>$

 

$<var>\boxed{d=\sqrt{97}}</var>$