Question

Determine a distância entre os pontos a e b, sendo:
A) a(-2,-4) e b(3,5)
B) a(0,5) e b(5,10)
C) a(raiz2, 4) e b(-3raiz2,5)

Answer 1

Resposta:

A)

$A(-2;-4)$

$B(3;5)$

$AB=B-A=(3;5)-(-2;-4)=(5;9)$

$\sqrt{5^2+9^2} =\sqrt{106}$

B)

$A(0;5)$

$B(5;10)$

$AB=B-A=(5;10)-(0;5)=(5;5)$

$\sqrt{5^2+5^2} =\sqrt{50}$

C)

$A(\sqrt{2};4)$

$B(-3\sqrt{2};5)$

$AB=B-A=(-3\sqrt{2};5)-(\sqrt{2};4)=(-3\sqrt{2}-\sqrt{2} ;1)$

$\sqrt{(-3\sqrt{2}-\sqrt{2})^2+1^2 } =\sqrt{9*2-2+1}=\sqrt{17}$

Explicação passo-a-passo:

$A(x;y)$

$B(a;b)$

$AB=B-A=(a;b)-(x;y)=(a-x;b-y)$

$\sqrt{(a-x)^2+(b-y)2}$