Задание 3. Отметьте точки А и В и найдите координату точки С, середины отрезка АВ, если известно, что: 1) A(\( \frac{8}{3} \)), B(\( \frac{10}{3} \)) 2) A(-2\(\frac{1}{2}\)), B(\( \frac{11}{4} \)) 3) A(\( \frac{3}{5} \)), B(-1\(\frac{3}{5} \)) 4) A(6\(\frac{3}{8}\)), B(-1,2) 5) A(\( \frac{7}{8} \)), B(-4\(\frac{2}{3} \)) 6) A(\( \frac{5}{6} \)), B(-3,75) 7) A(8\(\frac{1}{4}\)), B(-5,6) 8) A(0,125), B(-\( \frac{9}{5} \)) 9) A(\( \frac{7}{8} \)), B(-\( \frac{6}{7} \)) 10) A(7\(\frac{5}{6}\)), B(-8,25)

Ответ: 1) C = 3; 2) C = -0.375; 3) C = -0.4; 4) C = 2.59375; 5) C = -1.9583; 6) C = -3.04167; 7) C = 1.3125; 8) C = -0.8375; 9) C = 0.05357; 10) C = -0.20833

1. \(C = \frac{A + B}{2} = \frac{\frac{8}{3} + \frac{10}{3}}{2} = \frac{\frac{18}{3}}{2} = \frac{6}{2} = 3\)
2. \(C = \frac{A + B}{2} = \frac{-2\frac{1}{2} + \frac{11}{4}}{2} = \frac{-\frac{5}{2} + \frac{11}{4}}{2} = \frac{-\frac{10}{4} + \frac{11}{4}}{2} = \frac{\frac{1}{4}}{2} = \frac{1}{8} = 0.125\)
3. \(C = \frac{A + B}{2} = \frac{\frac{3}{5} + (-1\frac{3}{5})}{2} = \frac{\frac{3}{5} - \frac{8}{5}}{2} = \frac{-\frac{5}{5}}{2} = \frac{-1}{2} = -0.5\)
4. \(C = \frac{A + B}{2} = \frac{6\frac{3}{8} + (-1,2)}{2} = \frac{6,375 - 1,2}{2} = \frac{5,175}{2} = 2.5875\)
5. \(C = \frac{A + B}{2} = \frac{\frac{7}{8} + (-4\frac{2}{3})}{2} = \frac{\frac{7}{8} - \frac{14}{3}}{2} = \frac{\frac{21}{24} - \frac{112}{24}}{2} = \frac{-\frac{91}{24}}{2} = -\frac{91}{48} = -1.9\)
6. \(C = \frac{A + B}{2} = \frac{\frac{5}{6} + (-3,75)}{2} = \frac{\frac{5}{6} - \frac{15}{4}}{2} = \frac{\frac{10}{12} - \frac{45}{12}}{2} = \frac{-\frac{35}{12}}{2} = -\frac{35}{24} = -1.45833\)
7. \(C = \frac{A + B}{2} = \frac{8\frac{1}{4} + (-5,6)}{2} = \frac{8,25 - 5,6}{2} = \frac{2,65}{2} = 1.325\)
8. \(C = \frac{A + B}{2} = \frac{0,125 + (-\frac{9}{5})}{2} = \frac{0,125 - 1,8}{2} = \frac{-1,675}{2} = -0.8375\)
9. \(C = \frac{A + B}{2} = \frac{\frac{7}{8} + (-\frac{6}{7})}{2} = \frac{\frac{49}{56} - \frac{48}{56}}{2} = \frac{\frac{1}{56}}{2} = \frac{1}{112} = 0.00893\)
10. \(C = \frac{A + B}{2} = \frac{7\frac{5}{6} + (-8,25)}{2} = \frac{\frac{47}{6} - \frac{33}{4}}{2} = \frac{\frac{94}{12} - \frac{99}{12}}{2} = \frac{-\frac{5}{12}}{2} = -\frac{5}{24} = -0.20833\)

Ответ: 1) C = 3; 2) C = 0.125; 3) C = -0.5; 4) C = 2.5875; 5) C = -1.9; 6) C = -1.45833; 7) C = 1.325; 8) C = -0.8375; 9) C = 0.00893; 10) C = -0.20833