Tag Perpendicular -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Perpendicular” #123

🔗geometry-fig017

Figure geometry 017 Generated with Asymptote

unitsize(1cm);
import geometry;
dotfactor*=1.5;
linemargin=5mm;

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-1,1));
show(currentcoordsys);

point A=(-3,-1), B=(3,4);
line l1=line(A,B);

draw(l1,red);
dot("$A$",A,SE);
dot("$B$",B,NW);

point M=(2,-2);
dot("$M$",M);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="parallel(point,line)"/></asyxml>*/
draw(parallel(M,l1),red);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="perpendicular(point,line)"/></asyxml>*/
line perp=perpendicular(M,l1);
draw(perp);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="intersectionpoint(line,line)"/></asyxml>*/
point interp=intersectionpoint(l1,perp);
dot(interp,green);

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markrightangle(picture,point,point,point,real,pen,margin,filltype)"/></asyxml>*/
markrightangle(l1.A,interp,rotate(180,interp)*M,size=5mm);

draw(box((-5,-5),(5,5)),invisible);

🔗geometry-fig018

Figure geometry 018 Generated with Asymptote

unitsize(1cm);
import geometry;
dotfactor*=1.5;

currentcoordsys=cartesiansystem((0,0),i=expi(pi/8)*(1.5,0),j=expi(pi/8)*(0,1));
show(currentcoordsys);

point A=(-1,-3), B=(5,2);
line l1=line(A,B);

draw(l1,red);
dot("$A$",A,SE);
dot("$B$",B,NW);

point M=(3,-3);
dot("$M$",M);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="projection(line)"/></asyxml>*/
point P=projection(l1)*M;
dot("$P$",P,2W);
draw(M--P);
markrightangle(l1.A,P,M);


/*<asyxml><view file="modules/geometry.asy" type="transform" signature="vprojection(line,bool)"/></asyxml>*/
point Q=vprojection(l1)*M;
dot("$Q$",Q,2W);
draw(M--Q);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="hprojection(line,bool)"/></asyxml>*/
point R=hprojection(l1)*M;
dot("$R$",R,2W);
draw(M--R);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="projection(line,line,bool)"/></asyxml>*/
point S=projection(l1,line((0,0),(0,1)))*M;
dot("$S$",S,2W);
draw(M--S,red);

draw(box((-1,-4),(7,5)),invisible);

🔗geometry-fig025

Figure geometry 025 Generated with Asymptote

Show geometry/fig0250.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Segment | #Perpendicular

unitsize(2cm);
import geometry;
linemargin=5mm;

// currentcoordsys=cartesiansystem((2,1),i=(1,0.25),j=(-0.25,.75));
// show(li=Label("$\vec{\imath}$",align=S,EndPoint), currentcoordsys);

point A=(-1,-1), B=(1,0.5);
line l1=line(A,B);

draw("$(l_1)$",l1);
draw("$s_1$",(segment) l1, 2pt+red,
     marker(stickframe,markuniform(2,true)));

/*<asyxml><view file="modules/geometry.asy" type="line" signature="bisector(segment,real)"/></asyxml>*/
line bis=bisector((segment) l1);
draw(bis,red);

/*<asyxml><view file="modules/geometry.asy" type="void" signature="show(picture,line,pen)"/></asyxml>*/
show(bis,grey);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(line,real)"/></asyxml>*/
dot(point(bis,1.5));

draw(box(locate((-2,-2)),locate((2,2))),invisible);

🔗geometry-fig045

Figure geometry 045 Generated with Asymptote

import geometry;
size(10cm,0);

point c2=(13,5);
real r=4, R=abs(c2)-r;

circle[] C={circle(origin, 4), circle(c2,R)};
draw(C[0]^^C[1], blue);

segment s=segment(origin, c2);
draw(s, red, dot);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(line,real)"/></asyxml>*/
point T=curpoint(s,r/(r-R)*abs(c2));
dot(T);
/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangents(circle,point)"/></asyxml>*/
line[] tgt=tangents(C[1], T);
draw(tgt);

point[][] t= new point[2][2];
for (int i=0; i < 2 ; ++i)
  for (int j=0; j < 2; ++j) {
    /*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,circle)"/></asyxml>*/
    t[i][j]=intersectionpoints(C[i],tgt[j])[0];
    draw(C[i].C--t[i][j], dot);
    markrightangle(T, t[i][j], C[i].C, size=(i == 0 ? 2mm : 0));
  }

addMargins(cm/2,cm/2);

🔗geometry-fig113

Figure geometry 113 Generated with Asymptote

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,0.75));
// show(currentcoordsys);

triangle t=rotate(-20)*triangle((-1,0), (2,0), (0,2));
drawline(t, linewidth(bp));
label(t,alignFactor=4);

line bab=bisector(t.AB);
draw(bab, blue);
perpendicularmark(t.AB,bab,quarter=4);

line bac=bisector(t.AC);
draw(bac, blue);
perpendicularmark(t.AC,bac,quarter=4);

line bbc=bisector(t.BC);
draw(bbc, blue);
perpendicularmark(t.BC,bbc,quarter=4);