Answer to Question #314688 in Analytic Geometry for ABC2468

Question

find the distance between the point (1, 2) and the line y= 4x+ 1

Answer 1

Let d be the sought distance, then, if M(1,2) and l:4x-y+1=0

$d={\frac {|l_x*M_x+l_y*M_y+1|} {\sqrt{l_x^2+l_y^2}}}={\frac {|4*1-1*2+1|} {\sqrt{16+1}}}={\frac {3\sqrt{17}} {17}}$