1MA 05. RECTES EN EL PLA/1MA.05.4 Angles i distàncies 1MA.05.4.61Q Distància d'un punt a una recta Quina és la distància entre el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»?

Format de la resposta: radical simplificat

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<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>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>p_1</mi><mo>,</mo><mi>p_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>q_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>q_2</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>q_3</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>distància</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>p_1</mi><mo>,</mo><mi>p_2</mi><mo>)</mo><mo>,</mo><mi>q_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>q_2</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>q_3</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p_1</mi><mo>,</mo><mi>p_2</mi><mo>,</mo><mi>q_1</mi><mo>,</mo><mi>q_2</mi><mo>,</mo><mi>q_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>8</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>7</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>103</mn><mo>*</mo><msqrt><mn>89</mn></msqrt></mrow><mn>89</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La distància entre el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»p_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»p_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«/mrow»«/mstyle»«/math», i la recta es calcula amb l'expressió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mfrac»«/mrow»«/mstyle»«/math»

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