[tex]a)\\\\x+2y-1=0 , \ \ x+2y-6=0\\\\A=1,\ B=2,\ \ C_{1}=-1,\ \ C_{2}=-6\\\\gdy\ mamy\ 2\ proste\ rownolegle\ w\ postaci\ Ax+Bx+C=0,\ to\ aby \ obliczyc\ odleglosc\ miedzy\ nimi\\\\ korzystamy\ ze\ wzoru:\\\\d=\frac{|C_{1}-C_{2}|}{\sqrt{A^2+B^2}}\\\\d=\frac{|-1-(-6)|}{\sqrt{1^2+2^2}}\frac{|-1+6|}{\sqrt{1+4}}=\frac{|5 |}{\sqrt{5}}=\frac{5}{\sqrt{5}}*\frac{\sqrt{5}}{\sqrt{5}}=\frac{5\sqrt{5}}{5}=\sqrt{5}[/tex]
[tex]b)\\\\ 3x+4y+2=0 ,\ \ 3x+4y-8=0 \\\\A=3,\ B=4,\ C_{1}=2,\ C_{2}=-8\\\\d=\frac{|2-(-8)|}{\sqrt{3^2+4^2}}\frac{|2+8|}{\sqrt{9+16}}=\frac{|10 |}{\sqrt{25}}=\frac{10}{5}=2[/tex]
