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<font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-family: times new roman,times,serif; font-style: italic;">La ecuación principal de la recta <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«/math»</span> está dada por la ecuación #L1. Además, se sabe que es perpendicular a la recta <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«/math»</span> en el punto </span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-family: times new roman,times,serif; font-style: italic;"></span></span></font>#P2 .<br /><font size="4"><span style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Determina la ecuación principal de la recta </span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-family: times new roman,times,serif; font-style: italic;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«/math»</span></span></span></font><font size="4"><span style="font-style: italic;"><span style="font-family: times new roman,times,serif;"> :</span></span></font><br style="font-family: times new roman,times,serif; font-style: italic;" /> <div style="text-align: center;"><font size="4"><span style="font-family: times new roman,times,serif;"></span></font>#dib<br /></div><br /><br /><br />
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<font size="4"><span style="font-family: times new roman,times,serif;"><font size="4" style="font-style: italic;">Solución:<br /><br /></font></span></font><span style="font-style: italic;"><font size="4"><span style="font-family: times new roman,times,serif;">Recordemos que la condicionalidad de perpendicularidad entre rectas nos indica que:<br /><br />"Dos rectas son perpendiculares si y sólo si el producto de sus pendientes es igual a <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»1«/mn»«/math»</span>"<br /><br /></span></font></span> <table style="width: 408px; height: 91px;" border="1"><tbody> <tr> <td width="100%" valign="top"><span style="font-style: italic;"><font size="4"><span style="font-family: times new roman,times,serif;"> </span></font></span><font size="4"><span style="font-family: times new roman,times,serif;"> </span></font><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»§#8869;«/mo»«mo»§nbsp;«/mo»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§#8660;«/mo»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»1«/mn»«/msub»«mo»·«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«/math»</span> <br /> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»1«/mn»«/msub»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»§nbsp;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«/math»</span><br /> </td> </tr></tbody> </table><font size="4"><span style="font-family: times new roman,times,serif;"><br /><span style="font-style: italic;">De la ecuación de la recta </span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«/math»</span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;">, dada por la ecuación </span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#L1«/mi»«/math»</span></span></font>, <font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;">es posible determinar su respectiva pendiente</span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»m«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mi»#m1«/mi»«/math»</span></span></font>.<br /><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;"> Por la condicionalidad de perpendicularidad, tenemos que:<br /><br /></span></span></font> <div style="text-align: center;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»1«/mn»«/msub»«mo»·«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»E«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mi»#m1«/mi»«mo»§nbsp;«/mo»«mo»·«/mo»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«mi»#m1«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»L«/mi»«mi»u«/mi»«mi»e«/mi»«mi»g«/mi»«mi»o«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«msub»«mi»m«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mi»#m2«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»P«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/math»</span><br /></div><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;"> <br />Como ya conocemos la pendiente de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«/math»</span>, además del punto que tienen en común con la recta </span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«/math»</span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;"> cuyas coordenadas son <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P2«/mi»«/math»</span>, podemos aplicar la ecuación "punto-pendiente" que nos ayudará a determinar la ecuación solicitada.<br /><br /></span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;">Si reemplazamos en la fórmula las coordenadas respectivas y la pendiente obtenida, se tiene:<br /><br /></span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»-«/mo»«mi»#y2«/mi»«mo»=«/mo»«mi»#m2«/mi»«mo»·«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#x2«/mi»«mo»)«/mo»«/math»</span></span></font><br /><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;"></span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"> </span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#r1«/mi»«mo»=«/mo»«mi»#m2«/mi»«mo»·«/mo»«mo»(«/mo»«mi»#r4«/mi»«mo»)«/mo»«/math»</span></span></font> <span style="font-style: italic;"><span style="font-family: times new roman,times,serif;">/ <font size="4">desarrollando la ecuación de la derecha</font></span></span><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><span style="font-style: italic;"><span style="font-family: times new roman,times,serif;"><font size="4">, se obtiene:</font></span></span><br /><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#r1«/mi»«mo»=«/mo»«mi»#r5«/mi»«mo»+«/mo»«mi»#r8«/mi»«/math»</span></span></font> <span style="font-style: italic;"><span style="font-family: times new roman,times,serif;">/</span></span> <font size="4"><span style="font-style: italic;"><span style="font-family: times new roman,times,serif;">despejando la variable "y", se obtiene</span></span></font><br /><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»#r5«/mi»«mi»#c7«/mi»«mi»#r7«/mi»«/math»</span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><br /><span style="font-style: italic;">Por lo tanto, la ecuación principal de la recta que pasa por el punto #P2 y que es perpendicular a la recta cuya ecuación es<span style="font-weight: bold;"> </span></span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#L1«/mi»«/math»</span></span></font><font size="4"><span style="font-family: times new roman,times,serif;"><span style="font-style: italic;"><span style="font-weight: bold;"> </span>es:<br /><br /></span> </span></font> <div style="text-align: center;"><font size="4"><span style="font-family: times new roman,times,serif;"><font size="5"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#L2«/mi»«/math»</span></font></span></font><br /></div><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"></span></font><font size="4"><span style="font-family: times new roman,times,serif;"></span></font>
No, case is unimportant
Yes, case must match
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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">¡Excelente!</span></font>
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<div style="text-align: justify;"><b id="internal-source-marker_0.8875169802922755" style="color: rgb(0, 0, 0); text-transform: none; text-indent: 0px; letter-spacing: normal; word-spacing: 0px; white-space: normal; orphans: 2; widows: 2;"><span style="color: rgb(0, 0, 0); font-family: arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-style: italic;"><font size="4"><span style="font-family: times new roman,times,serif;">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</span></font></span></span></b></div>
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