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3=b\)</p>
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ã\(\mathrm{A,C,E}\)ã® \(x\) 座æ¨ã®å·®ï¼ééï¼ã 1ï¼3 ã«ãªãã¾ãã</p>
<p>ã\(\mathrm{A}\) ã® \(x\) 座æ¨ã¯\(-2\)ï¼\(\mathrm{E}\) ã® \(x\) 座æ¨ã¯ \(0\)<br />
ãªã®ã§ããã®å·®ã\(2\)ãã4çåããã°ãããããããªãã¾ãã<br />
ã\(\mathrm{A}\) 㨠\(\mathrm{E}\) ã®ä¸ç¹ã® \(x\) 座æ¨ã¯ \(-1\)<br />
ããã«ãã®ååå·¦ã«å¯ãã¨ç¹ \(\mathrm{C}\) ã® \(x\) 座æ¨ãªã®ã§,<br />
ã\(\mathrm{C}\) ã® \(x\) 座æ¨ã¯ã\(\displaystyle -\frac{3}{2}\)<br />
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<p>ãã® \(\mathrm{C}\) 㯠\(\ell\) ä¸ã®ç¹ãªã®ã§ \(y\) 座æ¨ããããã¾ãã<br />
ã \(\ellã:ã\displaystyle y=\frac{1}{2}x+3\)</p>
<p>ã« \(\displaystyle x=-\frac{3}{2}\)ããä»£å ¥ãã¦<br />
ã\(\begin{eqnarray}<br />
\displaystyle y&#038;=&#038;\frac{1}{2}\times \left(-\frac{3}{2}\right)+3\\<br />
\displaystyle &#038;=&#038;-\frac{3}{4}+3\\<br />
\displaystyle &#038;=&#038;\frac{-3+12}{4}\\<br />
\displaystyle &#038;=&#038;\frac{9}{4}<br />
\end{eqnarray}\)</p>
<p>ãã£ã¦ç¹\(\mathrm{C}\)ã®åº§æ¨ã¯<br />
ã\(\displaystyle \mathrm{C}\left(\,-\frac{3}{2}\,,\,\frac{9}{4}\,\right)\) ã</p>
<p>ãã®ç¹\(\mathrm{C}\)ã¯â¡ãéã£ã¦ãã¾ãã<br />
â¡ \(y=ax^2\) ã¯1ç¹ããã°æ¯ä¾å®æ°ã決ã¾ãã®ã§ç¹\(\mathrm{C}\)ãä»£å ¥ããã¨<br />
ã\(\begin{eqnarray}<br />
\displaystyle \frac{9}{4}&#038;=&#038;a\left(-\frac{3}{2}\right)^2\\<br />
\displaystyle \frac{9}{4}&#038;=&#038;\frac{9}{4}a\\<br />
1&#038;=&#038;a<br />
\end{eqnarray}\)</p>
<p>ã∴ã\(\underline{a=1}\)</p>
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<p><span class="red b">ã\(\ellãï¼ã\displaystyle y=\frac{1}{2}x+3\)<br />
ã\(\mathrm{A}\,(-2\,,\,2\,)\)ã\(\displaystyle \mathrm{B}\,\left(3\,,\,\frac{9}{2}\,\right)\)<br />
ã\(\displaystyle \mathrm{C}\,\left(-\frac{3}{2}\,,\,\frac{9}{4}\,\right)\)ã\(\mathrm{D}\,(2\,,\,4\,)\)</span></p>
<p>ããããã§ãã</p>
<p>ã<span class="black b">ç´ç· OC ã®å»¶é·ã¨æ²ç·â ã¨ã®äº¤ç¹ã F</span><br />
ã<span class="black b">ç´ç· OD ã®å»¶é·ã¨æ²ç·â ã¨ã®äº¤ç¹ã G</span></p>
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ã\(\displaystyle \frac{9}{4}=a\times \left(-\frac{3}{2}\right)\)<br />
ãããã<br />
ã\(\displaystyle a=-\frac{9}{4}\times \frac{2}{3}=-\frac{3}{2}\)</p>
<p>ãã£ã¦<span class="red b">ç´ç· OC ã¯ã \(\displaystyle y=-\frac{3}{2}x\)</span></p>
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ã\(4=a\times 2\)ãããã\(a=2\)</p>
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<p>ã\( \begin{cases}<br />
\hspace{7pt}\displaystyle y=\frac{1}{2}x^2\\<br />
\hspace{7pt}\displaystyle y=-\frac{3}{2}x<br />
\end{cases}\)</p>
<p>ãã<br />
ã\(\begin{eqnarray}<br />
\displaystyle \frac{1}{2}x^2&#038;=&#038;-\frac{3}{2}x\\<br />
x^2&#038;=&#038;-3x\\<br />
x^2+3x&#038;=&#038;0\\<br />
x(x+3)&#038;=&#038;0\\<br />
x&#038;=&#038;0,-3<br />
\end{eqnarray}\)</p>
<p>\(x=0\)ãã¯åç¹ã®ãã¨ãªã®ã§<span class="red b">äº¤ç¹ F ã® \(x\) 座æ¨ã¯ \(-3\)</span></p>
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ã\(\displaystyle y=-\frac{3}{2}\times (-3)=\frac{9}{2}\)</p>
<p>ãã£ã¦ã<span class="red b">\(\displaystyle \mathrm{F}\,\left(\,-3\,,\,\frac{9}{2}\right)\)</span></p>
<p>åãããã«ç¹ F ã¯ãâ ã¨ç´ç· OC ã¨ã®äº¤ç¹ã§ãã</p>
<p>ã\( \begin{cases}<br />
\hspace{7pt}\displaystyle y=\frac{1}{2}x^2\\<br />
\hspace{7pt} y=2x<br />
\end{cases}\)</p>
<p>ãã<br />
ã\(\begin{eqnarray}<br />
\displaystyle \frac{1}{2}x^2&#038;=&#038;2x\\<br />
x^2&#038;=&#038;4x\\<br />
x^2-4x&#038;=&#038;0\\<br />
x(x-4)&#038;=&#038;0\\<br />
x&#038;=&#038;0,4<br />
\end{eqnarray}\)</p>
<p>\(x=0\)ãã¯åç¹ã®ãã¨ãªã®ã§<span class="red b">äº¤ç¹ G ã® \(x\) 座æ¨ã¯ \(4\)</span></p>
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ã\(y=2\times (4)=8\)</p>
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ã\(\displaystyle \left(\hspace{6pt}-3\hspace{10pt},\hspace{10pt}\frac{9}{2}\hspace{10pt}\right)\)<br />
ã\((\hspace{15pt}4\hspace{12pt},\hspace{12pt}8\hspace{12pt})\)</p>
<p>ãã®2ç¹ãéãã®ã§ç´ç· FG ã1次é¢æ° \(y=ax+b\) ã¨ããã¨</p>
<p>ã\(\begin{eqnarray}<br />
\displaystyle a&#038;=&#038;\frac{8-(\frac{9}{2})}{4-(-3)}= \frac{\frac{7}{2}}{7}= \frac{7}{2}\times \frac{1}{7}\\<br />
\displaystyle &#038;=&#038; \frac{1}{2}<br />
\end{eqnarray}\)</p>
<p>ããããã\(\displaystyle y=\frac{1}{2}x+b\)</p>
<p>ããã«ç¹ F,G ã©ã¡ãããä»£å ¥ãã㨠\(b\) ãæ±ã¾ãã¾ãã<br />
ã\(\mathrm{G}\,(\,4\,,\,8\,)\)<br />
ãä»£å ¥ããã¨<br />
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8=2+b\)<br />
ããããã\(b=6\)</p>
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<img src="https://arakannotie.com/wp-content/uploads/2018/10/2018saitama424.jpg" alt="" width="484" height="374" class="aligncenter size-full wp-image-12644" /><br />
大ããä¸è§å½¢ OFG ããå°ããä¸è§å½¢ OCD ãå¼ãã¾ãã</p>
<p>ã\(åè§å½¢\mathrm{CDGF}ï¼\color{red}{\triangle \mathrm{OFG}} -\color{magenta}{\triangle \mathrm{OCD}}\)</p>
<p>ãã®é¢ç©è¨ç®ã¯ããããèãããã¾ãããä¸çªå¤ãå½¢ã§æ±ãã¦ã¿ã¾ãããã<br />
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<img src="https://arakannotie.com/wp-content/uploads/2018/10/2018saitama425.jpg" alt="" width="465" height="364" class="aligncenter size-full wp-image-12646" /><br />
ç´ç· FG ã®åçã H ã¨ããã¨ãåºè¾º OH ã¨ããä¸è§å½¢ã«2ã¤ã«åãããã¨ãã§ãã¾ãã</p>
<p>ã\(\color{red}{\triangle \mathrm{OFG}=\triangle \mathrm{OFH}+\triangle \mathrm{OGH}}\)</p>
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<p>é«ãã¯ã<br />
ã\(\color{red}{é ç¹ãã y 軸ã¸ã®åç·ã®é·ã}\)<br />
ã«ãªãã¾ãã®ã§<span class="red b">ããããã® \(x\) 座æ¨</span>ã§ãã</p>
<p>ãã£ã¦</p>
<p>ã\(\begin{eqnarray}<br />
\triangle \mathrm{\color{red}{OFG}}&#038;=&#038;\triangle \mathrm{OFH}+\triangle \mathrm{OGH}\\<br />
\displaystyle &#038;=&#038;\frac{1}{2}\times \color{blue}{6}\times \color{magenta}{3}+\frac{1}{2}\times \color{blue}{6} \times \color{magenta}{4}\\ &#038;=&#038;9+12\\<br />
&#038;=&#038;\color{red}{21}<br />
\end{eqnarray}\)</p>
<p>ããããã\(\color{magenta}{\triangle \mathrm{OCD}}\)ãã®é¢ç©ãå¼ãã°è¯ãã®ã§ãã<br />
<img src="https://arakannotie.com/wp-content/uploads/2018/10/2018saitama4262.jpg" alt="" width="397" height="318" class="aligncenter size-full wp-image-12648" /><br />
ã\(\begin{eqnarray}<br />
\color{magenta}{\triangle \mathrm{OCD}}&#038;=&#038;\triangle \mathrm{OCE}+\triangle \mathrm{ODE}\\<br />
\displaystyle &#038;=&#038;\frac{1}{2}\times \color{blue}{3}\times \color{magenta}{\frac{3}{2}}+\frac{1}{2}\times \color{blue}{3} \times \color{magenta}{2}\\<br />
\displaystyle &#038;=&#038;\frac{9}{4}+3\\<br />
\displaystyle &#038;=&#038;\frac{9+12}{4}\\<br />
&#038;=&#038;\color{magenta}{\frac{21}{4}}<br />
\end{eqnarray}\)ãã<br />
ã<br />
ãã£ã¦æ±ããåè§å½¢ CDGF ã®é¢ç©ã¯</p>
<p>ã\(\begin{eqnarray}<br />
åè§å½¢\mathrm{CDGF}&#038;=&#038;\color{red}{\triangle \mathrm{OFG}} -\color{magenta}{\triangle \mathrm{OCD}}\\<br />
\displaystyle &#038;=&#038;\color{red}{21}-\color{magenta}{\frac{21}{4}}\\<br />
\displaystyle &#038;=&#038;\frac{84-21}{4}\\<br />
\displaystyle (çã)&#038;=&#038;\frac{63}{4}\hspace{10pt}(\mathrm{cm^2})<br />
\end{eqnarray}\)</p>
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