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<p> </p> <p><span style="color: #000000;"><em><strong>L'altura d'un triangle és la recta perpendicular a un costat traçada des del vèrtex oposat. </strong></em></span></p> <p><span style="color: #000000;"><em><strong>L'ortocentre és el punt d'intersecció de les altures que corresponen als 3 vèrtex.</strong></em></span></p> <p> </p> <p><strong><span style="color: #003300;">En el triangle de vèrtex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math», </span></strong></p> <p><strong><span style="color: #003300;">a) Quina és l'equació explícita de l'altura traçada des del vèrtex A?</span></strong></p> <p><strong><span style="color: #003300;">b) Quina és l'equació explícita de l'altura traçada des del vèrtex B?</span></strong></p> <p><strong><span style="color: #003300;">c) Quines són les coordenades de l'ortocentre del triangle? <span style="color: #ff6600;">Format</span> </span></strong>(2,3)</p> <p> </p>
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<p><span style="color: #003300;"><strong>Gràficament:</strong> </span>#G1</p>
No, case is unimportant
Yes, case must match
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Answer 1
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Answer 2
Answer
Grade
None
100%
90%
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70%
66.66667%
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33.33333%
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Hint 1
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<div style="text-align: justify;"> </div> <div style="text-align: justify;"><span style="font-weight: bold; color: #000080;"><span style="font-weight: bold; color: #000080;">Com l'altura passa per A el que necessitem és el seu vector director; i c</span></span><span style="font-weight: bold; color: #000080;">om que aquesta altura és perpendicular al segment BC, el seu vector director és perpendicular al vector BC.</span></div> <div style="text-align: center;"> <div style="text-align: justify;"> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»BC«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»BC«/mi»«/mrow»«/mstyle»«/math»<span style="color: #000080;" data-mce-mark="1"><strong> i un vector perpendicular al segment BC és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»PBC«/mi»«/mstyle»«/math»</strong></span></div> <div style="text-align: justify;"><span style="color: #000080;" data-mce-mark="1"><strong>Fem el mateix per l'altura que passa per B, amb el vector perpendicular a AC: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»PAC«/mi»«/mrow»«/mstyle»«/math»</strong></span></div> <div style="text-align: justify;"> </div> <div style="text-align: justify;"> </div> <div style="text-align: justify;"><span style="color: #000080;" data-mce-mark="1"><strong>Gràficament:</strong></span> #G1</div> </div>
Hint 2
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<p><span style="color: #000080;"><strong>Resolem per igualació el sistema d'equacions format per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math» per trobar el seu punt d'intersecció per determinar l'ortocentre.</strong></span></p>
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