如图,平面直角坐标系中,A(4,-8) B(4,0)C(0,-6),点D为线段OB上一点,作DE//AC交AB于E,将直线AC向上平移交y轴负半轴于C‘交AB于A’,连DC',作EF//DC'交A'C'于F,若四边形DEFC'恰好为正方形时,则直线EF的函数表
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![如图,平面直角坐标系中,A(4,-8) B(4,0)C(0,-6),点D为线段OB上一点,作DE//AC交AB于E,将直线AC向上平移交y轴负半轴于C‘交AB于A’,连DC',作EF//DC'交A'C'于F,若四边形DEFC'恰好为正方形时,则直线EF的函数表](/uploads/image/z/7114533-69-3.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%AD%2CA%284%2C-8%29+B%284%2C0%29C%280%2C-6%29%2C%E7%82%B9D%E4%B8%BA%E7%BA%BF%E6%AE%B5OB%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%BD%9CDE%2F%2FAC%E4%BA%A4AB%E4%BA%8EE%2C%E5%B0%86%E7%9B%B4%E7%BA%BFAC%E5%90%91%E4%B8%8A%E5%B9%B3%E7%A7%BB%E4%BA%A4y%E8%BD%B4%E8%B4%9F%E5%8D%8A%E8%BD%B4%E4%BA%8EC%E2%80%98%E4%BA%A4AB%E4%BA%8EA%E2%80%99%2C%E8%BF%9EDC%27%2C%E4%BD%9CEF%2F%2FDC%27%E4%BA%A4A%27C%27%E4%BA%8EF%2C%E8%8B%A5%E5%9B%9B%E8%BE%B9%E5%BD%A2DEFC%27%E6%81%B0%E5%A5%BD%E4%B8%BA%E6%AD%A3%E6%96%B9%E5%BD%A2%E6%97%B6%2C%E5%88%99%E7%9B%B4%E7%BA%BFEF%E7%9A%84%E5%87%BD%E6%95%B0%E8%A1%A8)
如图,平面直角坐标系中,A(4,-8) B(4,0)C(0,-6),点D为线段OB上一点,作DE//AC交AB于E,将直线AC向上平移交y轴负半轴于C‘交AB于A’,连DC',作EF//DC'交A'C'于F,若四边形DEFC'恰好为正方形时,则直线EF的函数表
如图,平面直角坐标系中,A(4,-8) B(4,0)C(0,-6),点D为线段OB上一点,作DE//AC交AB于E,将直线AC向上平移交y轴负半轴于C‘交AB于A’,连DC',作EF//DC'交A'C'于F,若四边形DEFC'恰好为正方形时,则直线EF的函数表达式为--------
如图,平面直角坐标系中,A(4,-8) B(4,0)C(0,-6),点D为线段OB上一点,作DE//AC交AB于E,将直线AC向上平移交y轴负半轴于C‘交AB于A’,连DC',作EF//DC'交A'C'于F,若四边形DEFC'恰好为正方形时,则直线EF的函数表
过A(4,8)、C(0,-6)的直线AC解析式:Y=-1/2X-6,
过A’作A‘H‘⊥Y轴于H,过A作AH⊥Y轴于H,
ΔA’HC‘∽ΔC’OD,ΔACH≌ΔA’C‘H’,
∴OD/OC‘=C’H‘/A’H‘=CH/AH=1/2,
易得:ΔODC’≌ΔBED,∴OC‘=BD,
∴BE=OD=1/3OB=4/3,∴E(4,-4/3),
又直线C’D解析式为:Y=2X-8/3,
设直线EF:Y=2X+b,过E(4,-4/3),
∴-4/3=8+b,b=-28/3,
∴EF解析式:Y=2X-28/3.
[∵DEFC‘是正方形,∴DC’=DE,∠C'DE=90°,
∴∠ODC‘+∠BDE=90°,∵∠OC+ODC’=90°,
∴∠OC‘D=’BDE,∵∠DOC‘=∠EBD=90°,
∴ΔODC’≌ΔBED.]