Question

1) Ache a distância entre os pontos indicados:

A) A(5, 2) e B(12, 2)

B) C(3, -2) e D(-1, 4)

C) E (-1/2, 1/2) e F( 1/2, 3/2)

D) G(a, 3a) e H(3a, 2a), com a>0

E) I (√2, -3) E J(3√2, 5)

F) L(√5, √2) e M(3√5, 5√2)

Answer 1

(A)

$d = \sqrt{(12-5)^2 + (2-2)^2} d = \sqrt{7^2 + 0^2} d = \sqrt{49} d = 7$

(B)

$d = \sqrt{[3-(-1)]^2 + (-2-4)^2} d = \sqrt{4^2 + (-6)^2} d = \sqrt{16 + 36} d = \sqrt{52} d = 2\sqrt{13}$

(C)

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

(D)

$d = \sqrt{(a-3a)^2 + (3a-2a)^2} d = \sqrt{(-2a)^2 + a^2} d = \sqrt{4a^2 + a^2} d = \sqrt{5a^2} d = a\sqrt{5}$

(E)

$d = \sqrt{(\sqrt{2} - 3\sqrt{2})^2 + (-3-5)^2} d = \sqrt{(-2\sqrt{2})^2 + (-8)^2} d = \sqrt{8 + 64} d = \sqrt{72} d = 6\sqrt{2}$

(F)

$d = \sqrt{(\sqrt{5}-3\sqrt{5})^2 + (\sqrt{2} - 5\sqrt{2})^2} d = \sqrt{(-2\sqrt{5})^2 + (-4\sqrt{2})^2} d = \sqrt{20 + 32} d = \sqrt{52} d = 2\sqrt{13}$