1MA 04. VECTORS/1MA.04.5 Problemes amb vectors
1MA.04.5.62Q PuntSimètric
Determina les coordenades del punt simètric de A respecte a B amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨»B«/mi»«mo mathvariant=¨bold¨»(«/mo»«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»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math».
Format de la resposta: [-5,3]
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1.0000000
0.5000000
0
0
#v_42
<question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>-</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_2</mi><mo>-</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>v_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>v_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>m_1</mi><mo>,</mo><mi>m_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>m_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>16</mn><mo>,</mo><mn>32</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">
#v_42
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Si M és el punt simètric, es compleix que AM = 2 AB = (#v_1, #v_2)
Un cop calculat el vector AM, el punt M és l'extrem del vector AM; coneixem les seves components (#v_1, #v_2) i el seu origen (#a_1, #a_2)
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