originX = 400;
originY = 300;
origin is Circle(originX, originY, 5, "white", "black");
originText is Text("Origin", originX-5, originY+20, "black");

##comment
vectorPX is mouseClickX;
vectorPY is mouseClickY;
pointP is Circle(vectorPX, vectorPY, 5, "red", "black");
vectorP is Line(originX, originY, vectorPX, vectorPY, "red");
vectorPtext is Text("Position vector P", vectorPX, vectorPY-10, "red");

##scaled from pixels to more appropriate units
unit = 50; 

PXunits is ((vectorPX)-originX);	##the x component of P in units
PYunits is ((originY)-vectorPY);	##the y component of P in units

vectorPMagnitude is round((sqrt((PXunits*PXunits) + (PYunits*PYunits))),2);	##the magnitude of P
labelMagnitude is Text("Vector P Magnitude: ", 100, 400, "black");		##text label
labelMagnitudeValue is Text(vectorPMagnitude/unit, 310, 400, "black");		##text label

adjacentMagnitude is abs((vectorPY-originY));					##used in trig to work out the ADJ for cos(T)
angle is acos(adjacentMagnitude/vectorPMagnitude);				##value of the angle between the vertical and P
labelAngle is Text("Accute angle between vertical and vector: ", 100, 420, "black");	##text label
labelAngleValue is Text(angle, 310, 420, "black");				##text label

baseAX = 1;
baseAY = 0;
baseBX = 0;
baseBY = 1;

baseAvector is Line(originX, originY, originX+baseAX*unit, originY-baseAY*unit, "blue");
baseAtext is Text("A", originX+baseAX*unit+10, originY-baseAY*unit, lightblue);
baseBvector is Line(originX, originY, originX+baseBX*unit, originY-baseBY*unit, "blue");
baseBtext is Text("B", originX+baseBX*unit, originY-baseBY*unit-10, lightblue);

##coefficients for bases
det is ((baseAX*baseBY) - (baseBX*baseAY));
coefA is (((1/det)*baseBY*PXunits)-((1/det)*(1)*baseBX*PYunits));
coefB is (((1/det)*(baseAX*PYunits))-((1/det)*baseAY*PXunits));

##The coefficient text for the linear combinations

coefAText is Div("coefatext", 150, 500, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>"+coefA/unit+"</p>");
coefBText is Div("coefbtext", 300, 500, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>"+coefB/unit+"</p>");
plusSymb is Div("plus", 280, 500, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>\+</p>");

##Base vector labels
baseText is Div("basetext",200 ,450 ,1 ,1, "<p style=font-family:arial;position:fixed;font-size:20px;>Base A</p>");
baseText2 is Div("basetext2", 340, baseText.y, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>Base B</p>");

##A base vector
resultText is Div("resultText", 100, 500, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>P =&nbsp</p>");
vectorBrackXpos3 = 190;
vectorBrackYpos3 = 490-85;
vectorElem1Xpos3 is vectorBrackXpos3+28;
vectorElem1Ypos3 is vectorBrackYpos3+80;
vectorElem2Xpos3 is vectorBrackXpos3+28;
vectorElem2Ypos3 is vectorBrackYpos3+113;
vectorBrack3 is Div("Brack3",vectorBrackXpos3,vectorBrackYpos3,1,1,"<p style=font-family:arial;position:fixed;font-size:80px;>(&nbsp)</p>");
vecX3 is Div("vecx3",vectorElem1Xpos3,vectorElem1Ypos3,1,1,"<p style=font-family:arial;position:fixed;font-size:20px;>"+baseAX+"</p>");
vecY3 is Div("vecy3",vectorElem2Xpos3 ,vectorElem2Ypos3 ,1,1,"<p style=font-family:arial;position:fixed;font-size:20px;>"+baseAY+"</p>");

##B base vector
vectorBrackXpos4 = vectorBrackXpos3+150;
vectorBrackYpos4 = vectorBrackYpos3;
vectorElem1Xpos4 is vectorBrackXpos4+28;
vectorElem1Ypos4 is vectorBrackYpos4+80;
vectorElem2Xpos4 is vectorBrackXpos4+28;
vectorElem2Ypos4 is vectorBrackYpos4+113;
vectorBrack4 is Div("Brack4",vectorBrackXpos4,vectorBrackYpos4,1,1,"<p style=font-family:arial;position:fixed;font-size:80px;>(&nbsp)</p>");
vecX4 is Div("vecx4",vectorElem1Xpos4,vectorElem1Ypos4,1,1,"<p style=font-family:arial;position:fixed;font-size:20px;>"+baseBX+"</p>");
vecY4 is Div("vecy4",vectorElem2Xpos4 ,vectorElem2Ypos4 ,1,1,"<p style=font-family:arial;position:fixed;font-size:20px;>"+baseBY+"</p>");

ty1 = "";

alert is Div("ohdear", 100, 50, 1, 1, "<p style=font-family:arial;position:fixed;font-size:20px;>"+ty1+"</p>");
detzero is (((baseAX*baseBY)-(baseBX*baseAY))==0) ? ty1="Base Vectors are not a Basis: B is dependant on A" : ty1="";

x is Button("X", "Select P", 600, 100, true);


picture is [alert, plusSymb, coefBText, coefAText, vecX4, vecY4, vectorBrack4, resultSymbText, resultSymbText2, vectorBrack3, resultText, vecY3, vecX3, baseText2, vecX2, vecY2, vectorBrack2, vecX, vecY, vectorBrack1, baseText, linComText, baseAvector, baseAtext, baseBvector, baseBtext, origin, originText, pointP, vectorP, vectorPtext, labelMagnitude, labelMagnitudeValue, labelAngle, labelAngleValue];