\tikzmath{\t=-0.5;};
\tikzmath{\DistP=1;};
\tikzmath{\DistM=0.75;};

\tikzmath{\Dst=1;};
\tikzmath{\Dst=1;};

\tikzmath{\xp=-1;};
\tikzmath{\yp=-2;};

\tikzmath{\vx=3;};
\tikzmath{\vy=1;};

\coordinate (P0) at (\xp,\yp);

\coordinate (v) at (\vx,\vy);
\coordinate (n) at (-\vy,\vx);

\coordinate (P1) at ($(P0)+(v)$);
\coordinate (PN) at ($(P0)+(n)$);

\fill (P0) circle(2pt) node [below] {$P_0$};

\draw [-Latex,thick] (P0) -- ++(v);
\draw [-Latex,thick] (P0) -- ++(n);
\tkzLabelSegment[below](P0,P1) {$\underline{v}$};
\tkzLabelSegment[right](P0,PN)  {$\underline{n}$};

\tkzMarkRightAngle[](P1,P0,PN);

%
%Drawing title texts
%

\tikzmath{\DstP=1.25;};
\tikzmath{\DstM=0.75;};


%Point in positive halfplane
\coordinate (PPlus) at ($(P0)+\DstP*(n)$);

%Point in negative halfplane
\coordinate (PMinus) at ($(P0)-\DstM*(n)$);

\draw ($(P0)!\t!(P1)$) -- ($(P1)!\t!(P0)$) node [right] {$r: ax+by=c$};
\draw (PPlus) node[] {$H_+: ax+by>c$};
\draw (PMinus) node[] {$H_-: ax+by