Категория:Задачник Кузнецова Аналитическая геометрия Задача 14

В этой категории варианты Задачи 14, раздела "Аналитическая геометрия" в задачнике Кузнецова Л.А.

Варианты[править]

Найти точку ${\displaystyle M'}$ симметричную точке ${\displaystyle M}$ относительно прямой (для вариантов 1–15) или плоскости (для вариантов 16–31).

Задача	Условие
14-1	${\displaystyle M\left(0;\ -3;\ -2\right)}$	${\displaystyle {\frac {x-1}{1}}={\frac {y+1{,}5}{-1}}={\frac {z}{1}}}$
14-2	${\displaystyle M\left(2;\ -1;\ 1\right)}$	${\displaystyle {\frac {x-4{,}5}{1}}={\frac {y+3}{-0{,}5}}={\frac {z-2}{1}}}$
14-3	${\displaystyle M\left(1;\ 1;\ 1\right)}$	${\displaystyle {\frac {x-2}{1}}={\frac {y+1{,}5}{-2}}={\frac {z-1}{1}}}$
14-4	${\displaystyle M\left(1;\ 2;\ 3\right)}$	${\displaystyle {\frac {x-0{,}5}{0}}={\frac {y+1{,}5}{-1}}={\frac {z-1{,}5}{1}}}$
14-5	${\displaystyle M\left(1;\ 0;\ -1\right)}$	${\displaystyle {\frac {x-3{,}5}{2}}={\frac {y-1{,}5}{2}}={\frac {z}{0}}}$
14-6	${\displaystyle M\left(2;\ 1;\ 0\right)}$	${\displaystyle {\frac {x-2}{0}}={\frac {y+1{,}5}{-1}}={\frac {z+0{,}5}{1}}}$
14-7	${\displaystyle M\left(-2;\ -3;\ 0\right)}$	${\displaystyle {\frac {x+0{,}5}{1}}={\frac {y+1{,}5}{0}}={\frac {z-0{,}5}{1}}}$
14-8	${\displaystyle M\left(-1;\ 0;\ -1\right)}$	${\displaystyle {\frac {x}{-1}}={\frac {y-1{,}5}{0}}={\frac {z-2}{1}}}$
14-9	${\displaystyle M\left(0;\ 2;\ 1\right)}$	${\displaystyle {\frac {x-1{,}5}{2}}={\frac {y}{-1}}={\frac {z-2}{1}}}$
14-10	${\displaystyle M\left(3;\ -3;\ -1\right)}$	${\displaystyle {\frac {x-6}{5}}={\frac {y-3{,}5}{4}}={\frac {z+0{,}5}{0}}}$
14-11	${\displaystyle M\left(3;\ 3;\ 3\right)}$	${\displaystyle {\frac {x-1}{-1}}={\frac {y-1{,}5}{0}}={\frac {z-3}{1}}}$
14-12	${\displaystyle M\left(-1;\ 2;\ 0\right)}$	${\displaystyle {\frac {x+0{,}5}{1}}={\frac {y+0{,}7}{-0{,}2}}={\frac {z-2}{2}}}$
14-13	${\displaystyle M\left(2;\ -2;\ -3\right)}$	${\displaystyle {\frac {x-1}{-1}}={\frac {y+0{,}5}{0}}={\frac {z+1{,}5}{0}}}$
14-14	${\displaystyle M\left(-1;\ 0;\ 1\right)}$	${\displaystyle {\frac {x+0{,}5}{0}}={\frac {y-1}{0}}={\frac {z-4}{2}}}$
14-15	${\displaystyle M\left(0;\ -3;\ -2\right)}$	${\displaystyle {\frac {x-0{,}5}{0}}={\frac {y+1{,}5}{-1}}={\frac {z-1{,}5}{1}}}$
14-16	${\displaystyle M\left(1;\ 0;\ 1\right)}$	${\displaystyle 4x+6y+4z-25=0}$
14-17	${\displaystyle M\left(-1;\ 0;\ -1\right)}$	${\displaystyle 2x+6y-2z+11=0}$
14-18	${\displaystyle M\left(0;\ 2;\ 1\right)}$	${\displaystyle 2x+4y-3=0}$
14-19	${\displaystyle M\left(2;\ 1;\ 0\right)}$	${\displaystyle y+z+2=0}$
14-20	${\displaystyle M\left(-1;\ 2;\ 0\right)}$	${\displaystyle 4x-5y-z-7=0}$
14-21	${\displaystyle M\left(2;\ -1;\ 1\right)}$	${\displaystyle x-y+2z-2=0}$
14-22	${\displaystyle M\left(1;\ 1;\ 1\right)}$	${\displaystyle x+4y+3z+5=0}$
14-23	${\displaystyle M\left(1;\ 2;\ 3\right)}$	${\displaystyle 2x+10y+10z-1=0}$
14-24	${\displaystyle M\left(0;\ -3;\ -2\right)}$	${\displaystyle 2x+10y+10z-1=0}$
14-25	${\displaystyle M\left(1;\ 0;\ -1\right)}$	${\displaystyle 2y+4z-1=0}$
14-26	${\displaystyle M\left(3;\ -3;\ -1\right)}$	${\displaystyle 2x-4y-4z-13=0}$
14-27	${\displaystyle M\left(-2;\ -3;\ 0\right)}$	${\displaystyle x+5y+4=0}$
14-28	${\displaystyle M\left(2;\ -2;\ -3\right)}$	${\displaystyle y+z+2=0}$
14-29	${\displaystyle M\left(-1;\ 0;\ 1\right)}$	${\displaystyle 2x+4y-3=0}$
14-30	${\displaystyle M\left(3;\ 3;\ 3\right)}$	${\displaystyle 8x+6y+8z-22=0}$
14-31	${\displaystyle M\left(-2;\ 0;\ 3\right)}$	${\displaystyle 2x-2y+10z+1=0}$