[tex]D^{2} = \sqrt{(-4)^{2}+(1)^{2} }[/tex]Resposta:
A) [tex]\sqrt{34}[/tex]
B) 10
C) 4
D) 2[tex]\sqrt{5}[/tex]
E) [tex]\sqrt{17\\[/tex]
F) 7
Explicação passo a passo:
a)(-2,-1) (3,-4)
[tex]D^{2} = \sqrt{(xB-xA)^{2}+(yB-yA)^{2}[/tex]
[tex]D^{2} = \sqrt{(3-(-2))^{2}+(-4-(-1))^{2} }[/tex]
[tex]D^{2} = \sqrt{(3+2)^{2}+(-4+1)^{2}}[/tex]
[tex]D^{2} = \sqrt{(5)^{2}+(-3)^{2}[/tex]
[tex]}\sqrt{D}= \sqrt{(25+9)}[/tex]
[tex]D=\sqrt{34}[/tex]
b) (-4,3) (-4,(-7)
[tex]D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}[/tex]
[tex]D^{2} = \sqrt{(-4-(-4))^{2}+(-7-3)^{2} }[/tex]
[tex]D^{2} = \sqrt{(-4+4)^{2}+(-7-3)^{2} }[/tex]
[tex]D^{2} = \sqrt{(0)+(-10)^{2} }[/tex]
[tex]\sqrt{D} = \sqrt{100}[/tex]
D=10
c) (1,3) (-3,3)
[tex]D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}[/tex]
[tex]D^{2} = \sqrt{(-3-1)^{2}+(3-3)^{2} }[/tex]
[tex]D^{2} = \sqrt{(-4)^{2}+(0)^{2} }[/tex]
[tex]\sqrt{D} = \sqrt{(16) }[/tex]
D=4
d) (-1,4) (-2,-3)
[tex]D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}[/tex]
[tex]D^{2} = \sqrt{(2-(-1))^{2}+(-3-4)^{2} }[/tex]
[tex]D^{2} = \sqrt{(2+1)^{2}+(-3-4)^{2} }[/tex]
[tex]D^{2} = \sqrt{(-1)^{2}+(-7)^{2} }[/tex]
[tex]D^{2} = \sqrt{(1+49)} }[/tex]
[tex]\sqrt{D}= \sqrt{(50)} }[/tex]
D= 2[tex]\sqrt{5}[/tex]
e) (5,2) (1,3)
[tex]D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}[/tex]
[tex]D^{2} = \sqrt{(1-5)^{2}+(3-2)^{2} }[/tex]
[tex]D^{2} = \sqrt{(-4)^{2}+(1)^{2} }[/tex]
[tex]D^{2} = \sqrt{(16+1}[/tex]
[tex]\sqrt{D} = \sqrt{17}[/tex]
D= [tex]\sqrt{17}[/tex]
f) (-1,5) (-1, 12)
[tex]D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}[/tex]
[tex]D^{2} = \sqrt{(-1-(-1))^{2}+(12-5)^{2} }[/tex]
[tex]D^{2} = \sqrt{(-1+1))^{2}+(12-5)^{2} }[/tex]
[tex]D^{2} = \sqrt{(0))^{2}+(7)^{2} }[/tex]
[tex]\sqrt{D}=\sqrt{21}[/tex]
D=7
