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<title>A.II.4.77</title>
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<div class="feladat">
<b>Feladat: 4.77.</b><br /> <a name="komal_407fel_1928_12_102o" />[<a href="bib_box.php?mode=sne-s-j-&amp;citation_num=115" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num=115'); return false;">115</a>] Válasszuk az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi mathvariant="italic">OPQR</m:mi></m:mrow></m:math> paralelogramma <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>O</m:mi></m:mrow></m:math> csúcsát egy derékszögű

koordinátarendszer origójának. E rendszerre nézve legyen

<div style="text-align:center">a <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi mathvariant="italic">PQ</m:mi></m:mrow></m:math> egyenes egyenlete: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:mi>x</m:mi><m:mo>+</m:mo>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:mi>y</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:mrow></m:math>;

a <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi mathvariant="italic">QR</m:mi></m:mrow></m:math> egyenes egyenlete: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

<m:mi>x</m:mi><m:mo>+</m:mo>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

<m:mi>y</m:mi><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>.</m:mo></m:mrow></m:math>

</div>

Fejezzük ki a paralelogramma területét az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:mo>,</m:mo>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

<m:mo>,</m:mo>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:mo>,</m:mo>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

</m:mrow></m:math>

paraméterek függvényeként!
<br />&nbsp;<br /></div>
<div class="feladat">
<a name="_solution_komal_407fel_1928_12_102o" /><b>Megoldás: 4.77</b><br />
<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>1</m:mn></m:mrow>

<m:mrow><m:mo stretchy="false">&verbar;</m:mo>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

<m:mo>-</m:mo>

<m:msub><m:mrow><m:mi>u</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msub>

<m:msub><m:mrow><m:mi>v</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow>

</m:msub>

<m:mo stretchy="false">&verbar;</m:mo></m:mrow>

</m:mfrac>

</m:mrow></m:math>. Részletesebben lásd [<a href="bib_box.php?mode=sne-s-j-&amp;citation_num=115" target="bib_box" onclick="window.open('bib_box.php?mode=sne-s-j-&amp;citation_num=115','bib_box','toolbar=no,location=no,directories=no,status=no,menubar=no,width=600,height=150')">115</a>][407.

fel. 1928. 12. szám, 102. o.]
<br />&nbsp;<br />&nbsp;<br /></div>
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