step1. I'm sorry Bow Tao brother
step2. tonight forget to make a straight line from the point formulas do not come off from the title, so to decadent formula
step3. After the discovery does not prove decadent and self-closing, so decadent to prove
step4. proof read online, drop by the Chilean strike
step5. skyh was cold, and found their own humble
. Step6 studied the results of the month:
$$求d=dist(P(x_0,y_0),L(ax+by+c=0))$$
$$ disposed PQ \ bot L to Q, then \ vec {PQ} = (A, B), and set R (x, y) is any point on L $$
$$\begin{aligned}则d&=|\vec{PQ}|\\&=\frac{|\vec{PQ}·\vec{PR}|}{|\vec{PQ}|}\\&=\frac{|A(x-x_0)+B(y-y_0)|}{\sqrt{A^2+B^2}}\\&=\frac{|Ax_0+By_0-(Ax+By+C)+C|}{\sqrt{A^2+B^2}}\\&=\frac{|Ax_o+By_0+C|}{\sqrt{A^2+B^2}}\end{aligned}$$