[tex]|\overrightarrow{AB}|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\a)\\A(4, 0)\,,\quad B(7,-2)\\\\ |\overrightarrow{AB}|=\sqrt{(7-4)^2+(-2-0)^2}=\sqrt{3^2+(-2)^2} = \sqrt{9+4} =\sqrt{13}\\\\b)\\A(-4, 2)\,,\quad B(20,5)\\\\ |\overrightarrow{AB}|= \sqrt{(20+4)^2+(5-2)^2}=\sqrt{24^2+3^2}=\sqrt{576+9} = \sqrt{585}= 3\sqrt{65}[/tex]
[tex]c)\\ A(-\frac12, \frac14)\,,\quad B(1,-2)\\\\ |\overrightarrow{AB}|=\sqrt{(1+\frac12)^2+(-2-\frac14)^2}= \sqrt{(\frac32)^2+(-\frac94)^2} =\sqrt{\frac94+\frac{81}{16}} = \\\\= \sqrt{\frac{36}{16}+\frac{81}{16}} =\sqrt{\frac{117}{16}} =\frac{3\sqrt{13}}4[/tex]
