a)
[tex]|AB|=\sqrt{(-2-2)^{2}+(5-8)^{2} } =\sqrt{(-4)^{2} +(-3)^{2} } =\sqrt{16+9} =\sqrt{25}=5[/tex]
[tex]|BC|=\sqrt{(6-(-2))^{2}+(-1-5)^{2} } =\sqrt{8^{2} +(-6)^{2} } =\sqrt{64+36} =\sqrt{100}=10[/tex]
[tex]|AC|=\sqrt{(6-2)^{2}+(-1-8)^{2} } =\sqrt{4^{2} +(-9)^{2} } =\sqrt{16+81} =\sqrt{97}[/tex]
b)
[tex]|AB|=\sqrt{(5-(-3))^{2}+(-1-4)^{2} } =\sqrt{8^{2} +(-5)^{2} } =\sqrt{64+25} =\sqrt{89}[/tex]
[tex]|BC|=\sqrt{(5-5)^{2}+(9-(-1))^{2} } =\sqrt{0^{2} +10^{2} } =\sqrt{100} =10[/tex]
[tex]|AC|=\sqrt{(5-(-3))^{2}+(9-4)^{2} } =\sqrt{8^{2} +5^{2} } =\sqrt{64+25} =\sqrt{89}[/tex]
c)
[tex]|AB|=\sqrt{(0-(-2))^{2}+(6-1)^{2} } =\sqrt{2^{2} +5^{2} } =\sqrt{4+25} =\sqrt{29}[/tex]
[tex]|BC|=\sqrt{(6-0)^{2}+(2-6)^{2} } =\sqrt{6^{2} +(-4)^{2} } =\sqrt{36+16} =\sqrt{52}=2\sqrt{13}[/tex]
[tex]|AC|=\sqrt{(6-(-2))^{2}+(2-1)^{2} } =\sqrt{8^{2} +1^{2} } =\sqrt{64+1} =\sqrt{65}[/tex]
