点到直线的距离8：观察平行线常数项的差距
2015-11-18 02:08
本范例演示点到直线的距离，重点探讨平行线方程中常数项的差距与距离之间的关系。通过构造线段和多边形，直观展示线性函数图像中平行线的几何性质，帮助理解解析几何中直线方程常数项的几何意义。
所属专题
函数、方程式、参数式
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.172.0" id="5f9b1099-c353-4ff9-baf4-d40e9f4c2d7a" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1000" height="698" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.553" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="251" window="100,100,250,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="266" window="290,134,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="553" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1" size="437" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="28"/>
</gui>
<euclidianView>
<size width="553" height="600"/>
<coordSystem xZero="217.89041569041376" yZero="199.22441744274818" scale="37.66856837082226" yscale="37.66856837082233"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="437" height="600"/>
<coordSystem xZero="136.7821422711538" yZero="405.3709140863685" scale="20.598108967119412" yscale="20.598108967119433"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="n">
<value val="14"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-39" y="55"/>
<labelMode val="1"/>
<slider min="1" max="20" absoluteScreenLocation="true" width="200" x="75" y="226" fixed="false" horizontal="false" showAlgebra="false"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="If">
<input a0="(n > 7) ∧ (n < 17)" a1="(0.2 * abs(n - 12))" a2="1"/>
<output a0="n_p"/>
</command>
<element type="numeric" label="n_p">
<value val="0.4"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<element type="numeric" label="b">
<value val="4"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="a">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="c">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="L_Q" exp="(a * x) + (b * y) + c = 0" type="line" />
<element type="line" label="L_Q">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3" y="4" z="0"/>
<lineStyle thickness="7" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<element type="point" label="Q">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-37" y="33"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="P" exp="(n_p * (a, b))" type="point" />
<element type="point" label="P">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.2000000000000002" y="1.6" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="c_p" exp="(a * x(P)) + (b * y(P))" />
<element type="numeric" label="c_p">
<value val="10"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="L_p" exp="(a * x) + (b * y) = c_p" type="line" />
<element type="line" label="L_p">
<show object="true" label="false" ev="4"/>
<condition showObject="n > 4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3" y="4" z="-10"/>
<lineStyle thickness="7" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Segment">
<input a0="P" a1="Q"/>
<output a0="d"/>
</command>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.6" y="-1.2000000000000002" z="0"/>
<lineStyle thickness="7" type="20" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""" + d + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="0.8524238031424106" y="2.395217587102011" z="1"/>
</element>
<expression label="text2" exp=""" + (LaTeX[a]) + " x + " + LaTeX[b] + " y = " + LaTeX[c_p] + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<condition showObject="n > 6"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="1"/>
<startPoint x="2.8965683865517313" y="2.6606909096227014" z="1"/>
</element>
<expression label="text3" exp=""$" + (LaTeX[a]) + "x+" + LaTeX[b] + "y=" + LaTeX[c] + "$"" />
<element type="text" label="text3">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="1"/>
<startPoint x="0.7993291386382722" y="-0.9497462766586895" z="1"/>
</element>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-5.545483269606242" y="-9.63072392308527" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.3125270770062105" y="-9.604176590833202" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="4"/>
<output a0="poly1" a1="e" a2="f" a3="g" a4="h" a5="C" a6="D"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0.98"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.0265473322520684" y="7.858010346612453" z="75.5311104461156"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-7.858010346612453" y="-0.026547332252067957" z="17.916896430971867"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0.02654733225206707" y="-7.858010346612453" z="-13.78207907779754"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="7.858010346612454" y="0.026547332252067513" z="43.83213493734619"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2.2859797447541426" y="-1.7461662442207495" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-5.57203060185831" y="-1.7727135764728166" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text4" exp=""點代入可得平行線""/>
<element type="text" label="text4">
<show object="true" label="false" ev="40"/>
<condition showObject="n > 2"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-5.280009947085552" y="-3.524837505109389" z="1"/>
</element>
<expression label="text5" exp=""常數項的差距不等於距離""/>
<element type="text" label="text5">
<show object="true" label="false" ev="40"/>
<condition showObject="n > 10"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-5.294698027166602" y="-5.200008922636369" z="1"/>
</element>
<expression label="text6" exp=""此兩數的比值 $\frac{" + (LaTeX[c_p]) + "}{" + LaTeX[d] + "}$ 有何意義？"" />
<element type="text" label="text6">
<show object="true" label="false" ev="40"/>
<condition showObject="n > 16"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-5.200367950329344" y="-6.84325403661802" z="1"/>
</element>
<expression label="text7" exp=""$" + (LaTeX[c_p]) + "\neq" + LaTeX[d] + "$"" />
<element type="text" label="text7">
<show object="true" label="false" ev="40"/>
<condition showObject="n > 10"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-1.2713627770231173" y="-5.701718749779051" z="1"/>
</element>
</construction>
</geogebra>