Question

Помогите срочно дам 50 баллов. ​

Answer 1

$1)\ \ \vec{c}=\{6\ ;-2\}\ \ ,\ \ \vec{d}=\{1\ ;-2\, \}\\\\\vec{b}=\dfrac{1}{2}\vec{c}-\vec{d}=\{3-1\, ;\, -1+2\}=\{2\, ;\, 1\, \}\\\\\\2)\ \ C(2;1)\ ,\ \ D(5;5)\\\\R=CD=\sqrt{(5-2)^2+(5-1)^2}=\sqrt{3^2+4^2}=5\\\\\underline{(x-2)^2+(y-1)^2=25}$

$3)\ \ C(2;2)\ ,\ \ D(6;5)\ ,\ \ E(5;-2)\\\\a)\ \ CD=\sqrt{(6-2)^2+(5-2)^2}=\sqrt{4^2+3^2}=5\\\\CE=\sqrt{(5-2)^2+(-2-2)^2}=\sqrt{3^2+4^2}=5\\\\CD=CE\\\\b)\ \ CM\ -\ bissektrisa\ \ \to \ \ \ CM\perp DE\ ,\ \ DM=ME\\\\M\Big(\dfrac{6+5}{2}\ ;\ \dfrac{5-2}{2}\Big)\ \ ,\ \ \ M(5,5\ ;\ 1,5)\\\\CM:\ \ \dfrac{x-2}{5,5-2}=\dfrac{y-2}{1,5-2}\ \ ,\ \ \ \dfrac{x-2}{3,5}=\dfrac{y-2}{-0,5}\ \ ,\ \ \ \dfrac{x-2}{7}=\dfrac{y-2}{-1}\\\\\\-x+2=7y-14\ \ ,\ \ 7y=-x+16\ \ ,\ \ y=-\dfrac{1}{7}\, x+\dfrac{16}{7}$

$4)\ \ B(1;-3)\ ,\ C(2;0)\ \ ,\ \ A(\, 0\, ;\, y)\\\\M\Big(\dfrac{1+2}{2}\ ;\ \dfrac{-3+0}{2}\Big)\ \ ,\ \ M(1,5\ ;\ -1,5)\\\\AM\perp BC\ \ ,\ \ AB=AC\ ,\ \ BM=MC\ \ ,\ \ \overline{BC}=(1\ ;\ 3)\to \\\\AM:\ 1\cdot (x-1,5)+3\cdot (y+1,5)=0\\\\AM:\ x+3y+3=0\\\\A=AM\cap OY\ \ ,\ \ \left\{\begin{array}{l}x+3y=-3\\x=0\end{array}\right\ \ \left\{\begin{array}{ccc}y=-1\\x=0\end{array}\right\ \ \ A(0;-1)$