Question

1-Calcule, em cada caso, a distância entre os dois pontos dados:
a)(1, 3) e (9, 9)
b)(-3, 1) e (5, 14)
c)(-4, -2) e (0, 7)
d)(8, 3) e (-4, 8)

Answer 1

Resposta:

A distância entre dois pontos é dada pela fórmula:

$d_{AB} =\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }$

Resolvendo, temos que:

a)

$d_{AB} =\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }\\\\d_{AB} =\sqrt{(3-1 )^{2}+(9 -9 )^{2} }\\\\d_{AB} =\sqrt{(2)^{2}+( 0)^{2} }\\\\d_{AB} =\sqrt{4+0 }\\\\d_{AB} =\sqrt{4}\\\\d_{AB} =2$

b)

$d_{AB} =\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }\\\\d_{AB} =\sqrt{(1-(-3) )^{2}+(14 -5 )^{2} }\\\\d_{AB} =\sqrt{(4)^{2}+( 9)^{2} }\\\\d_{AB} =\sqrt{16+81 }\\\\d_{AB} =\sqrt{97}\\\\d_{AB} =9,84$

c)

$d_{AB} =\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }\\\\d_{AB} =\sqrt{(-2-(-4) )^{2}+(7 -0 )^{2} }\\\\d_{AB} =\sqrt{(2)^{2}+( 7)^{2} }\\\\d_{AB} =\sqrt{4+49 }\\\\d_{AB} =\sqrt{53}\\\\d_{AB} =7,28$

d)

$d_{AB} =\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }\\\\d_{AB} =\sqrt{(3-8 )^{2}+(8 -(-4) )^{2} }\\\\d_{AB} =\sqrt{(-5)^{2}+(12)^{2} }\\\\d_{AB} =\sqrt{25+144 }\\\\d_{AB} =\sqrt{169}\\\\d_{AB} =13$