Răspuns:
Folosim formula distanței dintre două puncte, atunci când cunoaștem coordonatele:
[tex]AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \\ [/tex]
[tex]= \sqrt{(3\sqrt{2} - 5\sqrt{2})^2 + (-1-1)^2} = \sqrt{( - 2\sqrt{2})^2 + (-2)^2} \\ [/tex]
[tex]= \sqrt{8 + 4} = \sqrt{12}[/tex]
[tex]CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \\[/tex]
[tex]= \sqrt{ \bigg(2+\dfrac{1}{2}\bigg)^2 + \bigg(-\dfrac{\sqrt{6}}{2} - \dfrac{\sqrt{6}}{2}\bigg)^2} = \sqrt{ \bigg(\dfrac{5}{2}\bigg)^2 + ( - \sqrt{6})^2}\\ [/tex]
[tex] = \sqrt{\dfrac{25}{4} + 6} = \sqrt{\dfrac{49}{4} } = \sqrt{12.5} \\ [/tex]
Cum 12 < 12,5, atunci
AB < CD
