A (4;2) ; B (-8;5)
1) Воспользуемся формулой нахождения координат вектора: вектор AB = {x₂-x₁ ; y₂-y₁}
Для удобства сделаем так: A (x₁;y₁) B (x₂;y₂)
Тогда решение: {-8-4 ; 5-2} = {-12;3}
2) Воспользуемся формулой нахождения длины вектора: вектор |OP| (то есть серединная прямая АВ) = √x²+y²
Тогда решение: OP = √(-8²)+5² = 64+25 = 89
3) Воспользуемся формулой нахождения координат середины отрезка: x = 
; y = 
Тогда: x = 
; y = 
4) Строим центр окружности на координатных прямых, радиус окружности которой равняется 4. Нам нужно уравнение окружности. (Сорян, построишь сам всё, села батарея на телефоне)
Формула уравнения: (x - a)² + (y - b)² = r², а известные нам значения: a = 5, b = -6, r = 4
Вставляем в уравнение и решаем:
(x-5)² + (y+6)² = 16, распишем.
x²-10x+25 + y²+12y+36 = 16
x²-10x+25 + y²+12y+20 = 0
Решаем дискриминанты:
1) x²-10x+25 = 0
D = b²-4ac => (-10²)-4*1*25 = 100-100 = 0=0, 1 корень.
x = 
x₁ = 
2) y²+12y+20 = 0
D = b²-4ac => 12²-4*1*20 = 144 - 80 = √64 = 8>0, 2 корня.
x = 
x₁ = 
x₂ = 
ответ: -10; -2; 5.
Пошаговое объяснение:
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-tv01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-tv02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-tv03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-tv04.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-jp01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-jp02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-jp03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-jp04.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-es01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-es02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-es03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-es04.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-It01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-It02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-It03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-It04.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-fr01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-fr02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-fr03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-fr04.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-gr01.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-gr02.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-gr03.html
http://www.borealoutdoor.com/bmc/video-poi-v-mcg-gr04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-tv01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-tv02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-tv03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-tv04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-jp01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-jp02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-jp03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-jp04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-es01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-es02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-es03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-es04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-It01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-It02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-It03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-It04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-fr01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-fr02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-fr03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-fr04.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-gr01.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-gr02.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-gr03.html
https://theshedcafe.com.au/uox/video-poi-v-mcg-gr04.html
