[tex]1. y- y_{A}=m(x- x_{A} ); x_{A}=2; y_{A}=-6, m=-2 \\ \\ y+6=m(x-2) \\ \\ [/tex]
[tex] 2.\frac{ x-x_{B} }{ x_{A}- x_{B}}= \frac{y-y_{B} }{ y_{A}- y_{B}} \\ \\ A(1,2); B(2,4); x_{A}=1; y_{A}=2; x_{B}=2; y_{B}=4; \\ \\ \frac{x-2}{1-2} = \frac{y-4}{2-4} \\ \\ \frac{x-2}{-1}= \frac{y-4}{-2} \\ \\ -2(x-2)=-1(y-4) \\ \\ -2x+4=-y+4 \\ \\ AB:-2x+y=0[/tex]
3.Distanţa de la punctul A (x0 , y0) la dreapta d: ax + by + c = 0 este
[tex] 2x-4y+5=0; a=2, b=-4, c=5 \\ \\ M(0,3); x_{0}=0; y_{0}=3 \\ \\ d(M,d)=\frac{ax_{0}+by_{0}+c}{ \sqrt{a^{2}+b^{2}} } \\ \\ [/tex][tex]d(M,d)=\frac{ax_{0}+by_{0}+c}{ \sqrt{a^{2}+b^{2}} } = \frac{2\cdot0+-4\cdot3+5}{ \sqrt {2^{2}+(-4)^{2} }} = \frac{-12+5}{ \sqrt{4+16}}= \frac{-7}{2 \sqrt{5} }= \frac{-7 \sqrt{5}}{10} [/tex]
