<?xml version="1.0" encoding="utf-8"?>
<CaR>
<Macro Name="Vect. mult. par un réel" showduplicates="true">
<Parameter name="E1">Coefficient multiplicateur</Parameter>
<Parameter name="s3">Vecteur</Parameter>
<Parameter name="E">Origine</Parameter>
<Objects>
<Point name="P1" n="0" parameter="true" x="0.701754385964913" y="1.3894736842105266">Point à 0.7, 1.39</Point>
<Point name="E" n="1" parameter="true" mainparameter="true" x="-0.7578947368421057" y="-2.624561403508772">Point à -0.76, -2.62</Point>
<Point name="P3" n="2" parameter="true" x="2.701754385964913" y="2.389473684210526">Point à 2.7, 2.39</Point>
<Expression name="E1" n="3" color="2" type="thick" parameter="true" mainparameter="true" x="0.0" y="0.0" value="1" prompt="Valeur">Expression &quot;1&quot; à 0.0, 0.0</Expression>
<Segment name="s3" n="4" color="2" parameter="true" mainparameter="true" from="P1" to="P3" arrow="true">Segment de P1 à P3</Segment>
<Point name="P4" n="5" color="2" showname="true" target="true" x="x(E)+E1*(x(P3)-x(P1))" actx="1.2421052631578942" y="y(E)+E1*(y(P3)-y(P1))" acty="-1.6245614035087725" shape="circle" fixed="true">Point à &quot;x(E)+E1*(x(P3)-x(P1))&quot;, &quot;y(E)+E1*(y(P3)-y(P1))&quot;</Point>
<Segment name="s2" n="6" color="2" target="true" from="E" to="P4" arrow="true">Segment de E à P4</Segment>
</Objects>
</Macro>
<Macro Name="Somme de deux vecteurs" showduplicates="true">
<Parameter name="s4">s4</Parameter>
<Parameter name="s5">s5</Parameter>
<Parameter name="E">E</Parameter>
<Objects>
<Point name="P1" n="0" parameter="true" x="-1.431578947368421" y="3.1298245614035105">Point à -1.43, 3.13</Point>
<Point name="P2" n="1" parameter="true" x="0.5333333333333332" y="3.831578947368421">Point à 0.53, 3.83</Point>
<Point name="P3" n="2" parameter="true" x="-2.8350877192982455" y="-0.6596491228070178">Point à -2.84, -0.66</Point>
<Point name="P4" n="3" parameter="true" x="-0.6175438596491236" y="-2.3157894736842106">Point à -0.62, -2.32</Point>
<Point name="E" n="4" parameter="true" mainparameter="true" x="0.28070175438596584" y="1.3894736842105266">Point à 0.28, 1.39</Point>
<Point name="P6" n="5" color="2" target="true" x="x(E)+x(P2)-x(P1)+x(P4)-x(P3)" actx="4.463157894736842" y="y(E)+y(P2)-y(P1)+y(P4)-y(P3)" acty="0.4350877192982443" shape="circle" fixed="true">Point à &quot;x(E)+x(P2)-x(P1)+x(P4)-x(P3)&quot;, &quot;y(E)+y(P2)-y(P1)+y(P4)-y(P3)&quot;</Point>
<Segment name="s4" n="6" color="2" parameter="true" mainparameter="true" from="P1" to="P2" arrow="true">Segment de P1 à P2</Segment>
<Segment name="s5" n="7" color="2" parameter="true" mainparameter="true" from="P3" to="P4" arrow="true">Segment de P3 à P4</Segment>
<Segment name="s3" n="8" color="2" target="true" from="E" to="P6" arrow="true">Segment de E à P6</Segment>
</Objects>
</Macro>
<Macro Name="Barycentre 2 pts">
<Parameter name="A">A</Parameter>
<Parameter name="a">a</Parameter>
<Parameter name="C">C</Parameter>
<Parameter name="c">c</Parameter>
<Comment>
<P>Désigner deux points pondérés (A,a) et (B,b) pour créer le
barycentre G=Bar{(A,a),(B,b)}</P>
</Comment>
<Objects>
<Point name="A" n="0" mainparameter="true" x="-2.7330316742081453" y="0.9230769230769229">Point à -2.73303, 0.92308 </Point>
<Expression name="a" n="1" color="1" type="thick" showvalue="true" mainparameter="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(A)+0.2" y="y(A)" value="2" prompt="" fixed="true">Expression &quot;2&quot; à -2.53303, 0.92308 </Expression>
<Point name="C" n="2" mainparameter="true" x="0.14479638009049722" y="0.16289592760180982">Point à 0.1448, 0.1629 </Point>
<Expression name="c" n="3" color="1" type="thick" showvalue="true" mainparameter="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(C)+0.2" y="y(C)" value="-1" prompt="" fixed="true">Expression &quot;-1&quot; à 0.3448, 0.1629 </Expression>
<Point name="P3" n="4" type="thick" target="true" bold="true" large="true" x="x(A)+c/(a+c)*(x(C)-x(A))" actx="-5.610859728506788" y="y(A)+c/(a+c)*(y(C)-y(A))" acty="1.683257918552036" shape="circle" fixed="true">Point à &quot;x(A)+c/(a+c)*(x(C)-x(A))&quot;, &quot;y(A)+c/(a+c)*(y(C)-y(A))&quot; </Point>
</Objects>
</Macro>
<Macro Name="Barycentre 3 pts">
<Parameter name="A">A</Parameter>
<Parameter name="a">a</Parameter>
<Parameter name="B">B</Parameter>
<Parameter name="b">b</Parameter>
<Parameter name="C">C</Parameter>
<Parameter name="c">c</Parameter>
<Comment>
<P>Désigner trois points pondérés (A,a) , (B,b) et (C,c) pour
créer le barycentre G=Bar{(A,a),(B,b),(C,c)}</P>
</Comment>
<Objects>
<Point name="A" n="0" mainparameter="true" x="-1.3465346534653468" y="3.514851485148516">Point à -1.34653, 3.51485 </Point>
<Expression name="a" n="1" color="1" type="thick" showvalue="true" mainparameter="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(A)+0.2" y="y(A)" value="2" prompt="" fixed="true">Expression &quot;2&quot; à -1.14653, 3.51485 </Expression>
<Point name="B" n="2" mainparameter="true" x="-2.7326732673267333" y="1.3762376237623757">Point à -2.73267, 1.37624 </Point>
<Expression name="b" n="3" color="1" type="thick" showvalue="true" mainparameter="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(B)+0.2" y="y(B)" value="3" prompt="" fixed="true">Expression &quot;3&quot; à -2.53267, 1.37624 </Expression>
<Point name="C" n="4" mainparameter="true" x="1.663366336633663" y="1.435643564356436">Point à 1.66337, 1.43564 </Point>
<Expression name="c" n="5" color="1" type="thick" showvalue="true" mainparameter="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(C)+0.2" y="y(C)" value="5" prompt="" fixed="true">Expression &quot;5&quot; à 1.86337, 1.43564 </Expression>
<Point name="P4" n="6" color="2" type="thick" hidden="super" showname="true" bold="true" large="true" ctag0="brown" cexpr0="1" ctag1="thick" cexpr1="1" x="x(A)+b/(a+b)*(x(B)-x(A))" actx="-2.178217821782179" y="y(A)+b/(a+b)*(y(B)-y(A))" acty="2.231683168316832" shape="circle" fixed="true">Point à &quot;x(P1)+E2/(E1+E2)*(x(P2)-x(P1))&quot;, &quot;y(P1)+E2/(E1+E2)*(y(P2)-y(P1))&quot; </Point>
<Expression name="E4" n="7" color="1" type="thick" hidden="super" showvalue="true" bold="true" large="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" x="x(P4)+0.2" y="y(P4)" value="a+b" prompt="Valeur" fixed="true">Expression &quot;E1+E2&quot; à -1.97822, 2.23168 </Expression>
<Point name="P5" n="8" color="2" type="thick" showname="true" target="true" bold="true" large="true" ctag0="brown" cexpr0="1" ctag1="thick" cexpr1="1" x="x(P4)+c/(E4+c)*(x(C)-x(P4))" actx="-0.2574257425742579" y="y(P4)+c/(E4+c)*(y(C)-y(P4))" acty="1.833663366336634" shape="circle" fixed="true">Point à &quot;x(P4)+E3/(E4+E3)*(x(P3)-x(P4))&quot;, &quot;y(P4)+E3/(E4+E3)*(y(P3)-y(P4))&quot; </Point>
</Objects>
</Macro>
<Construction>
<Window x="0.0" y="0.0" w="8.0"/>
<Windowdim w="800" h="600"/>
<Preferences minfontsize="12" minpointsize="2" minlinesize="1" arrowsize="15" digits.lengths="2" digits.edit="2" digits.angles="0" colorbackground="255,255,255"/>
<Objects>
<Point name="A" n="32" color="1" type="thick" showname="true" x="-2.2481012658227852" y="-2.744303797468355" shape="dcross">Point à -2.25, -2.74</Point>
<Point name="B" n="33" color="5" type="thick" showname="true" x="1.8632911392405058" y="-2.217721518987342" shape="dcross">Point à 1.86, -2.22</Point>
<Point name="C" n="89" color="2" type="thick" showname="true" xcoffset="0.3926271374639132" ycoffset="0.3506995336442369" keepclose="true" x="-0.3645569620253166" y="-0.9822784810126581" shape="dcross">Point à -0.36, -0.98</Point>
<Point name="P1" n="0" color="1" hidden="true" x="(windoww/(windoww-d(windoww)))*(x(P1)-windowcx)+windowcx+d(windowcx)" actx="-6.0" y="(windoww/(windoww-d(windoww)))*(y(P1)-windowcy)+windowcy+d(windowcy)" acty="3.0" shape="dcross" fixed="true">Point à &quot;(windoww/(windoww-d(windoww)))*(x(P1)-windowcx)+windowcx+d(windowcx)&quot;, &quot;(windoww/(windoww-d(windoww)))*(y(P1)-windowcy)+windowcy+d(windowcy)&quot;</Point>
<Point name="P7" n="11" color="1" hidden="true" x="(windoww/(windoww-d(windoww)))*(x(P7)-windowcx)+windowcx+d(windowcx)" actx="-6.0" y="(windoww/(windoww-d(windoww)))*(y(P7)-windowcy)+windowcy+d(windowcy)" acty="1.5" shape="dcross" fixed="true">Point à &quot;(windoww/(windoww-d(windoww)))*(x(P7)-windowcx)+windowcx+d(windowcx)&quot;, &quot;(windoww/(windoww-d(windoww)))*(y(P7)-windowcy)+windowcy+d(windowcy)&quot;</Point>
<Point name="P17" n="90" color="2" hidden="true" x="(windoww/(windoww-d(windoww)))*(x(P17)-windowcx)+windowcx+d(windowcx)" actx="-6.0" y="(windoww/(windoww-d(windoww)))*(y(P17)-windowcy)+windowcy+d(windowcy)" acty="0.0" shape="dcross" fixed="true">Point à &quot;(windoww/(windoww-d(windoww)))*(x(P17)-windowcx)+windowcx+d(windowcx)&quot;, &quot;(windoww/(windoww-d(windoww)))*(y(P17)-windowcy)+windowcy+d(windowcy)&quot;</Point>
<Point name="P2" n="1" color="1" hidden="true" bold="true" x="x(P1)+3*windoww" actx="18.0" y="y(P1)" acty="3.0" fixed="true">Point à &quot;x(A)+3*windoww&quot;, &quot;y(A)&quot; </Point>
<Point name="P8" n="12" color="1" hidden="true" bold="true" x="x(P7)+3*windoww" actx="18.0" y="y(P7)" acty="1.5" fixed="true">Point à &quot;x(A)+3*windoww&quot;, &quot;y(A)&quot; </Point>
<Point name="P18" n="91" color="2" hidden="true" bold="true" x="x(P17)+3*windoww" actx="18.0" y="y(P17)" acty="0.0" fixed="true">Point à &quot;x(A)+3*windoww&quot;, &quot;y(A)&quot; </Point>
<Segment name="s1" n="2" color="1" hidden="super" bold="true" from="P1" to="P2">Segment de P1 à P2</Segment>
<Segment name="s3" n="13" color="1" hidden="super" bold="true" from="P7" to="P8">Segment de P7 à P8</Segment>
<Segment name="s5" n="92" color="2" hidden="super" bold="true" from="P17" to="P18">Segment de P17 à P18</Segment>
<PointOn name="po3" n="3" color="1" hidden="true" xcoffset="0.023289245826246585" ycoffset="-0.3726279332199498" keepclose="true" bold="true" on="s1" alpha="0.0625" x="-4.5" y="3.0" shape="dcross">Point sur s1 </PointOn>
<PointOn name="po9" n="14" color="1" hidden="true" xcoffset="0.023289245826246585" ycoffset="-0.3726279332199498" keepclose="true" bold="true" on="s3" alpha="0.0625" x="-4.5" y="1.5" shape="dcross">Point sur s1 </PointOn>
<PointOn name="po19" n="93" color="2" hidden="true" xcoffset="0.023289245826246585" ycoffset="-0.3726279332199498" keepclose="true" bold="true" on="s5" alpha="0.0625" x="-4.5" y="0.0" shape="dcross">Point sur s1 </PointOn>
<Point name="P4" n="4" color="1" bold="true" x="x(po3)" actx="-4.5" y="y(po3)+windoww/20" acty="3.4" shape="cross" fixed="true">Point à &quot;x(po3)&quot;, &quot;y(po3)+windoww/20&quot; </Point>
<Point name="P10" n="15" color="5" bold="true" x="x(po9)" actx="-4.5" y="y(po9)+windoww/20" acty="1.9" shape="cross" fixed="true">Point à &quot;x(po3)&quot;, &quot;y(po3)+windoww/20&quot; </Point>
<Point name="P20" n="94" color="2" bold="true" x="x(po19)" actx="-4.5" y="y(po19)+windoww/20" acty="0.4" shape="cross" fixed="true">Point à &quot;x(po3)&quot;, &quot;y(po3)+windoww/20&quot; </Point>
<Point name="P5" n="5" color="1" bold="true" x="x(P4)+2*(x(P1)-x(po3))" actx="-7.5" y="y(P4)" acty="3.4" shape="cross" fixed="true">Point à &quot;x(P4)+2*(x(A)-x(po3))&quot;, &quot;y(P4)&quot; </Point>
<Expression name="E1" n="6" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P4)+windoww/30" y="y(P4)+windoww/25" value="-3" prompt="m" fixed="true">Expression &quot;-5&quot; à -1.74431, 0.11941 </Expression>
<Expression name="E2" n="7" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P4)+windoww/30" y="y(P4)-windoww/40" value="3" prompt="M" fixed="true">Expression &quot;5&quot; à -1.74431, -0.40059 </Expression>
<Point name="P11" n="16" color="5" bold="true" x="x(P10)+2*(x(P7)-x(po9))" actx="-7.5" y="y(P10)" acty="1.9" shape="cross" fixed="true">Point à &quot;x(P4)+2*(x(A)-x(po3))&quot;, &quot;y(P4)&quot; </Point>
<Expression name="E4" n="17" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P10)+windoww/30" y="y(P10)+windoww/25" value="-3" prompt="m" fixed="true">Expression &quot;-5&quot; à -1.74431, 0.11941 </Expression>
<Expression name="E5" n="18" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P10)+windoww/30" y="y(P10)-windoww/40" value="3" prompt="M" fixed="true">Expression &quot;5&quot; à -1.74431, -0.40059 </Expression>
<Point name="P21" n="95" color="2" bold="true" x="x(P20)+2*(x(P17)-x(po19))" actx="-7.5" y="y(P20)" acty="0.4" shape="cross" fixed="true">Point à &quot;x(P4)+2*(x(A)-x(po3))&quot;, &quot;y(P4)&quot; </Point>
<Expression name="E7" n="96" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P20)+windoww/30" y="y(P20)+windoww/25" value="-3" prompt="m" fixed="true">Expression &quot;-5&quot; à -1.74431, 0.11941 </Expression>
<Expression name="E8" n="97" color="1" type="thick" hidden="true" showname="true" showvalue="true" x="x(P20)+windoww/30" y="y(P20)-windoww/40" value="3" prompt="M" fixed="true">Expression &quot;5&quot; à -1.74431, -0.40059 </Expression>
<Segment name="s2" n="8" color="1" bold="true" from="P5" to="P4">Segment de P5 à P4</Segment>
<Segment name="s4" n="19" color="5" bold="true" from="P11" to="P10">Segment de P11 à P10</Segment>
<Segment name="s6" n="98" color="2" bold="true" from="P21" to="P20">Segment de P21 à P20</Segment>
<PointOn name="po6" n="9" color="2" xcoffset="4.583102756861024E-6" ycoffset="0.14519389194800736" keepclose="true" bold="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" on="s2" alpha="0.5734880450070321" x="-5.779535864978904" y="3.4" shape="circle">Point sur s2 </PointOn>
<PointOn name="po12" n="20" color="5" xcoffset="4.583102756861024E-6" ycoffset="0.14519389194800736" keepclose="true" bold="true" ctag0="thick" cexpr0="1" on="s4" alpha="0.4476289134438306" x="-6.157113259668508" y="1.9" shape="circle">Point sur s2 </PointOn>
<PointOn name="po22" n="99" color="2" xcoffset="4.583102756861024E-6" ycoffset="0.14519389194800736" keepclose="true" bold="true" ctag0="green" cexpr0="1" ctag1="thick" cexpr1="1" on="s6" alpha="0.6754385964912281" x="-5.473684210526316" y="0.4" shape="circle">Point sur s2 </PointOn>
<Expression name="a" n="10" color="1" type="thick" showname="true" showvalue="true" bold="true" large="true" x="x(po6)-windoww/100" y="y(po6)+windoww/30" value="round((E1+d(P5,po6)/d(P5,P4)*(E2-E1))*10)/10" prompt="a" fixed="true">Expression &quot;round((E1+d(P5,po6)/d(P5,P4)*(E2-E1))*10)/10&quot; à -2.75005, 0.06608 </Expression>
<Expression name="b" n="21" color="5" type="thick" showname="true" showvalue="true" bold="true" large="true" x="x(po12)-windoww/100" y="y(po12)+windoww/30" value="round((E4+d(P11,po12)/d(P11,P10)*(E5-E4))*10)/10" prompt="b" fixed="true">Expression &quot;round((E1+d(P5,po6)/d(P5,P4)*(E2-E1))*10)/10&quot; à -2.75005, 0.06608 </Expression>
<Expression name="c" n="100" color="1" type="thick" showname="true" showvalue="true" bold="true" large="true" x="x(po22)-windoww/100" y="y(po22)+windoww/30" value="round((E7+d(P21,po22)/d(P21,P20)*(E8-E7))*10)/10" prompt="c" fixed="true">Expression &quot;round((E1+d(P5,po6)/d(P5,P4)*(E2-E1))*10)/10&quot; à -2.75005, 0.06608 </Expression>
</Objects>
</Construction>
</CaR>
