Ребят, помогите срочно! Координаты: A(13;10) B(3;5) C(15;-4). Created by moetyan. matematika-ru

Ребят, помогите срочно! Координаты: A(13;10) B(3;5) C(15;-4)...

moetyan @moetyan

August 2022 1 16 Report

Ребят, помогите срочно!
Координаты:
A(13;10)
B(3;5)
C(15;-4)

Answers & Comments

NNNLLL54

Verified answer

$A(13,10)\; ,\; \; B(3,5)\; ,\; \; C(15,-4)\\\\1)\; \; \overline {AB}=(3-13,5-10)=(-10,-5)\; \; ,\; \; \vec{s}_{AB}=(5,1)\\\\|\overline {AB}|=\sqrt{10^2+5^2}=\sqrt{125}=5\sqrt5\\\\\overline {AC}=(15-13,-4-10)=(2,-14)\; \; ,\; \; \vec{s}_{AC}=(1,-7)\\\\|\overline {AC}|=\sqrt{2^2+14^2}=\sqrt{200}=10\sqrt2\\\\\overline {BC}=(15-3,-4-5)=(12,-9)\; \; ,\; \; \vec{s}_{BC}=(4,-3)\\\\|\overline {BC}|=\sqrt{12^2+9^2}=\sqrt{225}=15\\\\2)\; \; AB:\; \; \frac{x-3}{-10}=\frac{y-5}{-5}\; \; \Rightarrow \; \; \frac{x-3}{2}=\frac{y-5}{1}\\\\\vec{s}=(2,1)\; \; \Rightarrow \; \; \vec{n}=(-1,2)\; \; \; \Big (\; \vec{s}\cdot \vec{n}=0\; \Big )$

$x-3=2(y-5)\; \; \to \; \; y=\frac{1}{2}x+\frac{7}{2}\; \; \Rightarrow \; \; k= \frac{1}{2}\\\\AC:\; \; \frac{x-15}{2}=\frac{y+4}{-14}\; \; \to \; \; \frac{x-15}{1}=\frac{y+4}{-7}\\\\\vec{s}=(1,-7)\; \; \to \; \; \vec{n}=(7,1)\\\\-7(x-15)=y+4\; \; \to \; \; y=-7x+101\; \; \Rightarrow \; \; k=-7\\\\BC:\; \; \frac{x-3}{12}=\frac{y-5}{-9}\; \; \to \; \; \frac{x-3}{4}=\frac{y-5}{-3}\\\\\vec{s}=(4,-3)\; \; \to \; \; \vec{n}=(3,4)\\\\-3(x-3)=4(y-5)\; \; \to \; \; y=-\frac{3}{4}x+\frac{29}{4}\; \; \Rightarrow \; \; k=-\frac{3}{4}$

$3)\; \; cosC=\frac{(\overline {BC}\cdot \overline {AC})}{|\overline {BC}|\cdot |\overline {AC}|}=\frac{2\cdot 4+14\cdot 3}{15\cdot 10\sqrt2}=\frac{50}{150\sqrt2}=\frac{1}{3\sqrt2}\\\\\angle C=arccos\frac{1}{3\sqrt2}$

$4)\; \; AL:\; \; \vec{n}=\vec{s}_{BC}=(4,-3)\; ,\; \; 4(x-13)-3(y-10)=0\; ,\\\\4x-52-3y+30=0\\\\AL:\; \; 4x-3y-22=0\; ;\\\\5)\; \; BK:\; \; x_{K}=\frac{x_{A}+x_{C}}{2}=\frac{13+15}{2}=14\\\\y_{K}=\frac{y_{A}+y_{C}}{2}=\frac{10-4}{2}=3\; ,\qquad K(14,3)$

$\overline {BK}=(14-3,3-5)=(11,-2)\\\\BK:\; \; \frac{x-3}{11}=\frac{y-5}{-2}\; ,\; \; -2(x-3)=11(y-5)\; ,\; \; \underline {2x+11y=61}\\\\6)\; \; \vec{n}_{AL}=\vec{s}_{BC}=(4,-3)\; \; \to \; \; AL:\; \; 4(x-13)-3(y-10)=0\; ,\\\\AL:\; \; \underline {4x-3y=22}\\\\\left \{ {{2x+11y=61\, |\cdot (-2)} \atop {4x-3y=22\; \; \; \; }} \right. \oplus \left \{ {{2x=61-11y} \atop {-25y=-100}} \right.\; \left \{ {{x=8,5} \atop {y=4}} \right. \; \; P(8,5\, ;\, 4)$

$7)\; \; \vec{s}_{AC}=(1,-7)\; ,\; AC\parallel\; l\; ,\; \; P(8,5\, ;\, 4)\in l\\\\l:\; \; \frac{x-8,5}{1}=\frac{y-4}{-7}\\\\8)\; \; x_{A}=\frac{x_{T}+x_{C}}{2}\; ,\; \; x_{T}=2x_{A}-x_{C}=2\cdot 13-15=11\\\\y_{T}=2y_{A}-y_{С}=2\cdot 10+4=24\\\\T(11,24)$

2 votes Thanks 1

Answers & Comments

Verified answer

rebyata znayushie ekonomiku pomogite odnoj iz celej denezhnyh reform provodimyh g

zat esim zat esimni septelui srochno

rebyatpomogitesrochno najdite neopredelennye integrally

40 ballov anglijskij

dorogie znatoki himii vo skolko raz umenshitsya skorost okisleniya glyukozy pri

pomogite plz chemu ravny molyarnye massy ekvivalentov h2so4 h2so3mgoh2 i baoh

himikiorganika napishite uravnenie reakcii slozhnogo efira iz salicilovoj kislo

anglijskij 30 ballovaae734ee9b7d9565bc658ef5c1d19a33 97394

tovarishi himiki pomogite zhiry ih raznovidnosti i sposoby polucheniya napishite

anglijskij 40 ballovcb7920838431c4b1fb5949484a8d84e1 96316

рекомендуемые вопросы

Helpful Links

Helpful Social