Question

calcule a distância entre os pontos:
a) A (5,2) e B (3,4)
b) C (4,-2) e D (6,-3)
c) E (0,-3) e (4, -6)
d) G (5,4) e H (-1,-4)
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Answer 1

Explicação passo-a-passo:

A distância entre dois pontos é calculada da seguinte forma:

$d=\sqrt{(x_{b}-x_{a})^{2} +(y_{b}-y_{a})^{2} }$

a) A (5,2) e B (3,4)

$d=\sqrt{(3-5)^{2} +(4-2)^{2} }\\\\d=\sqrt{(-2)^{2} +2^{2} }\\\\d=\sqrt{4+4 }\\\\d=\sqrt{8} \\\\d=2\sqrt{2}$

b)C (4,-2) e D (6,-3)

$d=\sqrt{(6-4)^{2} +(-3-(-2))^{2} }\\\\d=\sqrt{2^{2} +(-1)^{2} }\\\\d=\sqrt{4+1} \\\\d=\sqrt{5}$

c) E (0,-3) e (4, -6)

$d=\sqrt{(4-0)^{2} +(-6-(-3))^{2} }\\\\d=\sqrt{4^{2} +(-3)^{2} }\\\\d=\sqrt{16+9} \\\\d=\sqrt{25} \\\\d=5$

d)G (5,4) e H (-1,-4)

$d=\sqrt{(-1-5)^{2} +(-4-4)^{2}}\\\\d=\sqrt{(-6)^{2} +(-8)^{2} }\\\\d=\sqrt{36+64} \\\\d=\sqrt{100} \\\\d=10$