Bài 3: Đồ thị của hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mo>&#160;</mo><mfenced><mrow><mi>a</mi><mo>&#160;</mo><mo>&#8800;</mo><mn>0</mn></mrow></mfenced></math>
Hướng dẫn giải Bài 15 (Trang 51 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 15 (Trang 51 SGK To&aacute;n 9, Tập 1):</strong></p> <p>a) Vẽ đồ thị của c&aacute;c h&agrave;m số:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><mi>x</mi><mo>;</mo><mo>&#160;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mn>5</mn><mo>;</mo><mo>&#160;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#160;</mo><mi>v</mi><mi>&#224;</mi><mo>&#160;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn></math> tr&ecirc;n c&ugrave;ng một mặt phẳng tọa độ.</p> <p>b) Bốn đường thẳng tr&ecirc;n cắt nhau tạo th&agrave;nh tứ gi&aacute;c OABC (O l&agrave; gốc tọa độ). Tứ gi&aacute;c OABC c&oacute; phải l&agrave; h&igrave;nh b&igrave;nh h&agrave;nh kh&ocirc;ng? V&igrave; sao ?</p> <p>&nbsp;</p> <p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p> <p><strong>a)</strong></p> <p>Với h&agrave;m số y = 2x: cho x = 1 =&gt; y = 2.1 = 2 ta được M(1; 2).</p> <p>Với h&agrave;m số y = 2x + 5:</p> <p>&nbsp; &nbsp; +) Cho x = -2,5 =&gt; y = 2(-2,5) + 5 = 0 ta được E(-2,5; 0)</p> <p>&nbsp; &nbsp; +) Cho x = 0 =&gt; y = 5 ta được B(0; 5)</p> <p><img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/24022022/5122b7e2-3173-4abd-bb18-e0212df3e21f.PNG" /></p> <p>-) Với h&agrave;m số&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>,</mo><mo>&#160;</mo><mi>c</mi><mi>h</mi><mi>o</mi><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>&#160;</mo><mo>&#8658;</mo><mo>&#160;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>.</mo><mn>1</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>&#8658;</mo><mo>&#160;</mo><mi>T</mi><mi>a</mi><mo>&#160;</mo><mi>&#273;</mi><mi>&#432;</mi><mi>&#7907;</mi><mi>c</mi><mo>&#160;</mo><mi>&#273;</mi><mi>i</mi><mi>&#7875;</mi><mi>m</mi><mo>&#160;</mo><mi>N</mi><mfenced><mrow><mn>1</mn><mo>;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced><mo>.</mo></math></p> <p>-) Với h&agrave;m số&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mo>:</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi>C</mi><mi>h</mi><mi>o</mi><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#8658;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>,</mo><mo>&#160;</mo><mi>t</mi><mi>a</mi><mo>&#160;</mo><mi>&#273;</mi><mi>&#432;</mi><mi>&#7907;</mi><mi>c</mi><mo>&#160;</mo><mi>&#273;</mi><mi>i</mi><mi>&#7875;</mi><mi>m</mi><mo>&#160;</mo><mi>B</mi><mfenced><mrow><mn>0</mn><mo>;</mo><mn>5</mn></mrow></mfenced><mspace linebreak="newline"/><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi>C</mi><mi>h</mi><mi>o</mi><mo>&#160;</mo><mi>y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#8658;</mo><mi>x</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>&#160;</mo><mi>t</mi><mi>a</mi><mo>&#160;</mo><mi>&#273;</mi><mi>&#432;</mi><mi>&#7907;</mi><mi>c</mi><mo>&#160;</mo><mi>&#273;</mi><mi>i</mi><mi>&#7875;</mi><mi>m</mi><mo>&#160;</mo><mi>F</mi><mfenced><mrow><mn>7</mn><mo>,</mo><mn>5</mn><mo>;</mo><mn>0</mn></mrow></mfenced></math></p> <p>Dựng c&aacute;c điểm M(1;2), E(-2,5;0), B(0;5),&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi><mfenced><mrow><mn>1</mn><mo>;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math>, F(7,5;0) tr&ecirc;n mặt phẳng tọa độ.</p> <p>+) Vẽ đường thẳng y = 2x qua O v&agrave; M(1;-2).</p> <p>+) Vẽ đường thẳng y = 2x + 5 qua B(0;5) v&agrave; E(-2,5;0)</p> <p>+) Vẽ đường thẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mi>qua</mi><mo>&#160;</mo><mi mathvariant="normal">O</mi><mo>&#160;</mo><mi>v&#224;</mi><mo>&#160;</mo><mi mathvariant="normal">N</mi><mfenced><mrow><mn>1</mn><mo>;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced><mo>.</mo></math></p> <p>+) Vẽ đường thẳng y<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mi>qua</mi><mo>&#160;</mo><mi mathvariant="normal">B</mi><mo>(</mo><mn>0</mn><mo>;</mo><mn>5</mn><mo>)</mo><mo>&#160;</mo><mi>v&#224;</mi><mo>&#160;</mo><mi mathvariant="normal">F</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>5</mn><mo>;</mo><mn>0</mn><mo>)</mo></math></p> <div class="ads_ads ads_2"><ins id="982a9496-1353c29425a79255e99fea2f719d8207-1-7695" class="982a9496" data-key="1353c29425a79255e99fea2f719d8207"><ins id="982a9496-1353c29425a79255e99fea2f719d8207-1-7695-1"> <div id="yomedia-passback-456df4d0f0e64616ab4c39ad529aaa0d-1645712195523"> <div id="div-ub-vietjack"></div> </div> </ins></ins></div> <p>&nbsp;</p> <p><strong>b)</strong></p> <p>Bốn đường thẳng đ&atilde; cho cắt nhau tại c&aacute;c điểm O, A.</p> <p>V&igrave; đường thẳng y = 2x + 5 song song với đường thẳng y = 2x, đường thẳng&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mi>song</mi><mo>&#160;</mo><mi>song</mi><mo>&#160;</mo><mi>v&#7899;i</mi><mo>&#160;</mo><mi>&#273;&#432;&#7901;ng</mi><mo>&#160;</mo><mi>th&#7859;ng</mi><mo>&#160;</mo><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="normal">x</mi></math>.</p> <p>Vậy tứ gi&aacute;c OABC l&agrave; h&igrave;nh b&igrave;nh h&agrave;nh (c&oacute; hai cặp cạnh song song).</p>
Hướng dẫn Giải Bài 15 (trang 51, SGK Toán 9, Tập 1)
GV: GV colearn
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Hướng dẫn Giải Bài 15 (trang 51, SGK Toán 9, Tập 1)
GV: GV colearn