Question

1) Calcule a distância entre os pontos dados :
a) A(-7,6) e B(5,-3)
b) B(3,7) e C(2,6)
c) H(0,-2) e I(√5,-2)
d) J(-4,0) e K(0,3)
pfvrr alguém ajuda



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Answer 1

Resposta:

a) 15

b) $\sqrt{2}$

c) $\sqrt{6}$

d) 5

Explicação passo-a-passo:

$a) d_{AB} = \sqrt{((-7)_{}-5_{})^{2}+(6_{}-(-3)_{})^{2}}\\d_{AB} = \sqrt{(-12)^{2}+(9)^{2}}\\d_{AB} = \sqrt{144+81}\\d_{AB} = \sqrt{225}\\d_{AB} =15$

$b) d_{AB} = \sqrt{(3_{}-2_{})^{2}+(7_{}-6_{})^{2}}\\d_{AB} = \sqrt{1^{2}+1^{2}}\\d_{AB} = \sqrt{2}$

$c) d_{AB} = \sqrt{(0_{}-\sqrt{5} _{})^{2}+((-2)_{}-(-2)_{})^{2}}\\d_{AB} = \sqrt{(-\sqrt{5} )^{2}+0^{2}}\\d_{AB} = \sqrt{\sqrt{25} +1}\\d_{AB} = \sqrt{5+1}\\d_{AB} = \sqrt{6}$

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