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Resposta passo a passo:

QUESTÃO 1:

A) A(-4,3), B(1,1)

[tex]d_{AB} =\sqrt{(1-(-4))^{2}+(1-3)^{2} } \\\\\\d_{AB} =\sqrt{(1+4)^{2}+(-2)^{2} } \\\\\\d_{AB} =\sqrt{5^{2}+(-2)^{2} } \\\\\\d_{AB} =\sqrt{25+4 } \\\\\\\bold{d_{AB} =\sqrt{29} }[/tex]

B) A(1,2), B(4,3)

[tex]d_{AB} =\sqrt{(4-1)^{2}+(3-2)^{2} } \\\\\\d_{AB} =\sqrt{3^{2}+1^{2} } \\\\\\d_{AB} =\sqrt{9+1 } \\\\\\\bold{d_{AB} =\sqrt{10} }[/tex]

C) A(0,0), B(5,5)

[tex]d_{AB} =\sqrt{(5-0)^{2}+(5-0)^{2} } \\\\\\d_{AB} =\sqrt{5^{2}+5^{2} } \\\\\\d_{AB} =\sqrt{5^{2} \times2} \\\\\\ d_{AB} =\sqrt{5^{2} }\times\sqrt{2} \\\\\\\bold{d_{AB} =5\sqrt{2} }[/tex]

D) A(-1,0), B(2,3)

[tex]d_{AB} =\sqrt{(2-(-1))^{2}+(3-0)^{2} } \\\\\\ d_{AB} =\sqrt{(2+1)^{2}+3^{2} } \\\\\\d_{AB} =\sqrt{3^{2}+3^{2} } \\\\\\ d_{AB} =\sqrt{3^{2} \times2 } \\\\\\ d_{AB} =\sqrt{3^{2} }\sqrt{2} \\\\\\\bold{d_{AB} =3\sqrt{2} }[/tex]

E) A(-2,3), B(5,2)

[tex]d_{AB} =\sqrt{(5-(-2))^{2}+(2-3)^{2} }\\\\\\d_{AB} =\sqrt{(5+2)^{2}+(-1)^{2} } \\\\\\d_{AB} =\sqrt{7^{2}+1 } \\\\\\d_{AB} =\sqrt{49+1 } \\\\\\d_{AB} =\sqrt{50} \\\\\\d_{AB} =\sqrt{25\times2} \\\\\\d_{AB} =\sqrt{25}\times\sqrt{2} \\\\\\d_{AB} =\sqrt{5^{2} }\sqrt{2} \\\\\\\bold{d_{AB} =5\sqrt{2} }[/tex]

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QUESTÃO 2:

A) A(-4,3), B(1,1)

[tex]P_{M} =(\frac{-4+1}{2} ,\ \frac{3+1}{2} ) \\\\P_{M} =(\frac{-3}{2} ,\ \frac{4}{2} ) \\\\\bold{P_{M} =(-\frac{3}{2} ,\ 2 )}[/tex]

B) A(1,2), B(4,3)

[tex]P_{M} =(\frac{1+4}{2} ,\ \frac{2+3}{2} ) \\\\\bold{P_{M} =(\frac{5}{2} ,\ \frac{5}{2} )}[/tex]

C) A(0,0), B(5,5)

[tex]P_{M} =(\frac{0+5}{2} ,\ \frac{0+5}{2} ) \\\\\bold{P_{M} =(\frac{5}{2} ,\ \frac{5}{2} )}[/tex]

D) A(-1,0), B(2,3)

[tex]P_{M} =(\frac{-1+2}{2} ,\ \frac{0+3}{2} ) \\\\\bold{P_{M} =(\frac{1}{2} ,\ \frac{3}{2} )}[/tex]

E) A(-2,3), B(5,2)​

[tex]P_{M} =(\frac{-2+5}{2} ,\ \frac{3+2}{2} ) \\\\\bold{P_{M} =(\frac{3}{2} ,\ \frac{5}{2} )}[/tex]

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https://brainly.com.br/tarefa/54008525

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