Bài 5: Hệ số góc của đường thẳng <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 30 (Trang 59 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 30 (Trang 59 SGK To&aacute;n 9, Tập 1):</strong></p> <p>a) Vẽ tr&ecirc;n c&ugrave;ng một mặt phẳng tọa độ đồ thị của c&aacute;c h&agrave;m số sau:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi mathvariant="normal">y</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>.</mo></math></p> <p>&nbsp;</p> <p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p> <p>a)</p> <p>- Vẽ đường thẳng y = -x + 2</p> <p>Cho x = 0 =&gt; y = 2, ta được điểm E(0;2)</p> <p>Cho y = 0 =&gt; x = 2, ta được điểm F(2;0).</p> <p>Nối 2 điểm EF v&agrave; k&eacute;o d&agrave;i ta được đường thẳng y = -x + 2</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><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn></math></p> <p>Cho x = 0 =&gt; y = 2, ta được điểm E(0;2)</p> <p>Cho y = 0 =&gt; x = -4, ta được điểm H(-4;0).</p> <p>Nối 2 điểm EH lại ta được 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><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn></math></p> <p>Vẽ đồ thị:</p> <p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/26102022/bai-30-trand-59-sdk-toan-9-tap-1-1-ztgnoD.jpg" /></p> <p>b)</p> <p>V&igrave; A l&agrave; giao điểm của 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><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn></math> với trục ho&agrave;nh n&ecirc;n&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>&#8801;</mo><mi mathvariant="normal">H</mi></math></p> <p>V&igrave; B l&agrave; giao điểm của y = -x + 2 với trục ho&agrave;nh n&ecirc;n&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mo>&#8801;</mo><mi mathvariant="normal">F</mi></math></p> <p>V&igrave; C l&agrave; giao điểm của hai đường thẳng n&ecirc;n&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>&#8801;</mo><mi mathvariant="normal">E</mi></math></p> <p>Ta c&oacute;:</p> <p>OA = 4cm, OC = 2cm, OB = 2cm, AB = 6cm.</p> <p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/26102022/bai-30-trand-59-sdk-toan-9-tap-1-2-0xPx5n.jpg" /></p> <p>Ta x&eacute;t tam gi&aacute;c COB vu&ocirc;ng tại O c&oacute; OC = OB = 2cm =&gt; Tam gi&aacute;c OCB vu&ocirc;ng c&acirc;n tại O =&gt;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>OCB</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mover><mi>OBC</mi><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>45</mn><mo>&#176;</mo></math></p> <p>Ta x&eacute;t tam gi&aacute;c AOC vu&ocirc;ng tại O c&oacute;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mo>&#160;</mo><mover><mrow><mi>C</mi><mi>A</mi><mi>O</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mi>C</mi><mi>O</mi></mrow><mrow><mi>A</mi><mi>O</mi></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>4</mn></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&#160;</mo><mo>&#8658;</mo><mo>&#160;</mo><mover><mrow><mi>C</mi><mi>A</mi><mi>O</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>26</mn><mo>&#176;</mo></math></p> <p>Ta x&eacute;t tam gi&aacute;c ACB c&oacute;:&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>C</mi><mi>B</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mover><mrow><mi>C</mi><mi>B</mi><mi>A</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mover><mrow><mi>C</mi><mi>A</mi><mi>B</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>180</mn><mo>&#176;</mo><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><mover><mrow><mi>A</mi><mi>C</mi><mi>B</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>26</mn><mo>&#176;</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>45</mn><mo>&#176;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>180</mn><mo>&#176;</mo><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><mover><mrow><mi>A</mi><mi>C</mi><mi>B</mi></mrow><mo>^</mo></mover><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>109</mn><mo>&#176;</mo></math></p> <p>c)</p> <p>X&eacute;t tam gi&aacute;c CAO vu&ocirc;ng tại O, ta c&oacute;:</p> <p>AO<sup>2</sup> + OC<sup>2</sup> = AC<sup>2</sup> (theo định l&iacute; Py-ta-go trong tam gi&aacute;c vu&ocirc;ng)</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8660;</mo><mo>&#160;</mo><msup><mn>4</mn><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><msup><mn>2</mn><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mi>AC</mi><mn>2</mn></msup><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><msup><mi>AC</mi><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>20</mn><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><mi>AC</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p>X&eacute;t tam gi&aacute;c CBO vu&ocirc;ng tại O, ta c&oacute;:</p> <p>OB<sup>2</sup> + OC<sup>2</sup> = BC<sup>2</sup> (theo định l&iacute; Py-ta-go trong tam gi&aacute;c vu&ocirc;ng)</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8660;</mo><mo>&#160;</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><mo>&#160;</mo><msup><mn>2</mn><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mi>BC</mi><mn>2</mn></msup><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><msup><mi>BC</mi><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>8</mn><mo>&#160;</mo><mo>&#8660;</mo><mo>&#160;</mo><mi>BC</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></math></p> <p>Chu vi tam gi&aacute;c ABC l&agrave;: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mi>AB</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>BC</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>AC</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><mo>(</mo><mn>3</mn><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><msqrt><mn>2</mn></msqrt><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><msqrt><mn>5</mn></msqrt><mo>)</mo><mo>&#160;</mo><mo>(</mo><mi>cm</mi><mo>)</mo></math></p> <p>Diện t&iacute;ch tam gi&aacute;c ABC l&agrave;:&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">S</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>AB</mi><mo>.</mo><mi>CO</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>.</mo><mn>6</mn><mo>.</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><mo>&#160;</mo><mo>(</mo><msup><mi>cm</mi><mn>2</mn></msup><mo>)</mo></math></p>
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