find the distance between the point (1, 2) and the line y= 4x+ 1
Let d be the sought distance, then, if M(1,2) and l:4x-y+1=0
d=∣lx∗Mx+ly∗My+1∣lx2+ly2=∣4∗1−1∗2+1∣16+1=31717d={\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}}d=lx2+ly2∣lx∗Mx+ly∗My+1∣=16+1∣4∗1−1∗2+1∣=17317
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