Respostas

2014-05-19T08:24:07-03:00
A(5,5)      B(3,-4)        C(-7,2/3)

distância de (A) até (B)

d _{ab} = \sqrt{(x_a-x_b)^2+(y_a-y_b)^2} \\  \\ d_a_b=  \sqrt{(5-3)^2+(5-(-4))^2}  \\  \\ d_a_b= \sqrt{4+81}  \\  \\ d_a_b= \sqrt{85}

distância de (A) até (C)

d _{ac} = \sqrt{(x_a-x_c)^2+(y_a-y_c)^2} \\ \\ d_a_c= \sqrt{(5-(-7))^2+(5- \frac{2}{3} )^2} \\ \\ d_a_c= \sqrt{144+ \frac{169}{9} } \\ \\ d_a_c= \sqrt{ \frac{1465}{9} } \\  \\ d_a_c = \frac{ \sqrt{1465} }{3}

distância de (B) até (C)

d _{bc} = \sqrt{(x_b-x_c)^2+(y_b-y_c)^2} \\ \\ d_b_c= \sqrt{(3-(-7))^2+(-4- \frac{2}{3} )^2} \\ \\ d_b_c= \sqrt{100+ \frac{196}{9} } \\ \\ d_b_c= \sqrt{ \frac{1096}{9} } \\ \\ d_b_c = \frac{2. \sqrt{274} }{3}