Kenneth McCown & Erik KatzenMinimum Distance Between a Point and a LineMath 152 - 202restart;with(Maplets[Tools]): with(Maplets[Elements]): with(plots):# with(plottools):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):pointcoord:=rand(-8..8):num1:=rand(-3..3):num2:=rand(-6..6):num3:=rand(-7..7):problem:=proc()
global dist2, derDist2, answerX, answerY, finalDist;
local co1, co2, co3, curve1, x1, x2, y1, y2, plotcrv, plotpt, curveplot;
co1:=num1():
co2:=num2():
while co2=0 do
co2:=num2():
end do;
co3:=num3():
curve1:=co2*x+co3;
x2:=x; y2:=curve1;
answerX:=2,3;
while nops([answerX])<>1 do
x1:=pointcoord();
y1:=pointcoord();
dist2:=(x2-x1)^2+(y2-y1)^2;
derDist2:=diff(dist2, x);
answerX:=solve(derDist2=0,x);
end do;
answerY:=eval(curve1,x=answerX);
finalDist:=sqrt(eval(dist2,x=answerX));
Set(TFcurv=curve1);
Set(TFpt=[x1,y1]);
plotcrv:=plot(curve1,x=-10..10, y=-10..10);
plotpt:=plot([[x1,y1]], style=point, symbol=circle, symbolsize=16, color=blue);
curveplot:=display([plotcrv,plotpt], axes=normal, tickmarks=[5,5], scaling=constrained);
Set(CurvePlot=curveplot);
Set(TFd2="");
Set(TFderiv="");
Set(TFx="");
Set(TFy="");
Set(TFd="");
Set(reply="");
end proc:hint1:=proc()
Set(reply="Add the square of the difference between the x-coordinates with the square of the difference between the y-coordinates."):
end proc:check1:=proc()
global dist2;
local user_d2;
if Get(TFd2)="" then
Set(reply="No answer given.");
return;
end if;
user_d2:=Get(TFd2::anything):
if simplify(dist2 - user_d2)=0 then
Set(reply="You're right!"):
else
Set(reply="Nope, try again."):
end if;
end proc:show1:=proc()
Set(TFd2=dist2):
Set(reply="Way to just surrender there."):
end proc:hint2:=proc()
Set(reply="Take the derivative of D^2 using the chain rule."):
end proc:check2:=proc()
global derDist2;
local user_deriv;
if Get(TFderiv)="" then
Set(reply="No answer given.");
return;
end if;
user_deriv:=Get(TFderiv::anything):
if simplify(derDist2 - user_deriv)=0 then
Set(reply="Way to go!"):
else
Set(reply="That's not even close."):
end if;
end proc:show2:=proc()
Set(TFderiv=derDist2):
Set(reply="You did try to do it at least once, right?."):
end proc:hint3:=proc()
Set(reply="Find the x-coordinate that allows the derivative formula to be equal to zero."):
end proc:check3:=proc()
global answerX;
local user_x;
if Get(TFx)=""then
Set(reply="No answer given.");
return;
end if;
user_x:=Get(TFx::anything):
if simplify(answerX - user_x=0) then
Set(reply="You got it!"):
else
Set(reply="In espanol: No."):
end if;
end proc:show3:=proc()
Set(TFx=answerX):
Set(reply="C'mon, it's not that hard."):
end proc:hint4:=proc()
Set(reply="Plug the x-coordinate into the equation of the line."):
end proc:check4:=proc()
global answerY;
local user_y;
if Get(TFy)="" then
Set(reply="No answer given.");
return;
end if;
user_y:=Get(TFy::anything):
if simplify(answerY - user_y=0) then
Set(reply="You're a freakin' genius!"):
else
Set(reply="It could be that your life really does have a purpose...even if that purpose is just to serve as a warning to others."):
end if;
end proc:show4:=proc()
Set(TFy=answerY):
Set(reply="Try it on your own next time."):
end proc:hint5:=proc()
Set(reply="Plug the values of x and y into the original distance formula, y=sqrt((x2-x1)^2+(y2-y1)^2)."):
end proc:check5:=proc()
global finalDist;
local user_d;
if Get(TFd)="" then
Set (reply="No answer given.");
return;
end if;
user_d:=Get(TFd::anything):
if simplify(finalDist - user_d=0) then
Set (reply="You're the next Einstein!"):
else
Set (reply="Just look at it this way...we can't all be rocket scientists when we grow up."):
end if;
end proc:show5:=proc()
Set(TFd=simplify(finalDist)):
Set(reply="Don't give up so fast."):
end proc:DistCurve:=Maplet(onstartup=RunWindow(MAIN),
Font[helv10]("helvetica",10),
Window[MAIN](title="Minimum Distance Between a Point and a Line",
[ [ Button("New Problem", Evaluate(function=problem), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ border=true,
"Find the point on the line y =",
TextField[TFcurv](width=16, editable=false, background=white),
"that is closest to the point",
TextField[TFpt](width=6, editable=false, background=white),
"and solve for that minimum distance."
],
[ halign=none, inset=0, spacing=0,
[ halign=none, inset=0, spacing=0,
[ border=true,
caption="Enter the square of the Distance Formula:",
"D^2 =",
TextField[TFd2](width=17, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint1"), background=yellow),
Button("Check", Evaluate(function="check1"), background=green),
Button("Show", Evaluate(function="show1"), background=lightorange)
],
[ border=true,
caption="Enter the derivative of the formula:",
"d/dx D^2 =",
TextField[TFderiv](width=17, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint2"), background=yellow),
Button("Check", Evaluate(function="check2"), background=green),
Button("Show", Evaluate(function="show2"), background=lightorange)
],
[ border=true,
caption="Find the x-coordinate which gives minimum distance:",
"x =",
TextField[TFx](width=8, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint3"), background=yellow),
Button("Check", Evaluate(function="check3"), background=green),
Button("Show", Evaluate(function="show3"), background=lightorange)
],
[ border=true,
caption="Find the y-coordinate which gives minimum distance:",
"y =",
TextField[TFy](width=8, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint4"), background=yellow),
Button("Check", Evaluate(function="check4"), background=green),
Button("Show", Evaluate(function="show4"), background=lightorange)
],
[ border=true,
caption="Find the distance between the origin and this point along the curve:",
"D =",
TextField[TFd](width=10, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint5"), background=yellow),
Button("Check", Evaluate(function="check5"), background=green),
Button("Show", Evaluate(function="show5"), background=lightorange)
]
],
[ border=true,
caption="Plot",
Plotter[CurvePlot](width=200, height=200)
]
],
[ halign=none,
TextField[reply](width=65, editable=false, background=white)
],
[ halign=none, background=ColorFooter,
Label("Programmers: Kenneth McCown & Erik Katzen", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
)
):Maplets[Display]( DistCurve );