已知y=-2分之1x+1交X轴于点A,交y轴于点B,将直线y=2x沿x轴方向平移,平移后交x轴于点C交y轴于点D,交y=-2分之1x+1于点p(1)当直线平移多少个单位,使△PBD与△AOB全等?(2)当直线平移多少个单位,△P
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![已知y=-2分之1x+1交X轴于点A,交y轴于点B,将直线y=2x沿x轴方向平移,平移后交x轴于点C交y轴于点D,交y=-2分之1x+1于点p(1)当直线平移多少个单位,使△PBD与△AOB全等?(2)当直线平移多少个单位,△P](/uploads/image/z/9592913-65-3.jpg?t=%E5%B7%B2%E7%9F%A5y%3D-2%E5%88%86%E4%B9%8B1x%2B1%E4%BA%A4X%E8%BD%B4%E4%BA%8E%E7%82%B9A%2C%E4%BA%A4y%E8%BD%B4%E4%BA%8E%E7%82%B9B%2C%E5%B0%86%E7%9B%B4%E7%BA%BFy%3D2x%E6%B2%BFx%E8%BD%B4%E6%96%B9%E5%90%91%E5%B9%B3%E7%A7%BB%2C%E5%B9%B3%E7%A7%BB%E5%90%8E%E4%BA%A4x%E8%BD%B4%E4%BA%8E%E7%82%B9C%E4%BA%A4y%E8%BD%B4%E4%BA%8E%E7%82%B9D%2C%E4%BA%A4y%3D-2%E5%88%86%E4%B9%8B1x%2B1%E4%BA%8E%E7%82%B9p%EF%BC%881%EF%BC%89%E5%BD%93%E7%9B%B4%E7%BA%BF%E5%B9%B3%E7%A7%BB%E5%A4%9A%E5%B0%91%E4%B8%AA%E5%8D%95%E4%BD%8D%2C%E4%BD%BF%E2%96%B3PBD%E4%B8%8E%E2%96%B3AOB%E5%85%A8%E7%AD%89%3F%EF%BC%882%EF%BC%89%E5%BD%93%E7%9B%B4%E7%BA%BF%E5%B9%B3%E7%A7%BB%E5%A4%9A%E5%B0%91%E4%B8%AA%E5%8D%95%E4%BD%8D%2C%E2%96%B3P)
已知y=-2分之1x+1交X轴于点A,交y轴于点B,将直线y=2x沿x轴方向平移,平移后交x轴于点C交y轴于点D,交y=-2分之1x+1于点p(1)当直线平移多少个单位,使△PBD与△AOB全等?(2)当直线平移多少个单位,△P
已知y=-2分之1x+1交X轴于点A,交y轴于点B,将直线y=2x沿x轴方向平移,平移后交x轴于点C交y轴于点D,交
y=-2分之1x+1于点p
(1)当直线平移多少个单位,使△PBD与△AOB全等?
(2)当直线平移多少个单位,△PAC的面积为4?
已知y=-2分之1x+1交X轴于点A,交y轴于点B,将直线y=2x沿x轴方向平移,平移后交x轴于点C交y轴于点D,交y=-2分之1x+1于点p(1)当直线平移多少个单位,使△PBD与△AOB全等?(2)当直线平移多少个单位,△P
(1)
y= - x/2 + 1, A(2, 0), B(0, 1), 斜率为-1/2
直线y=2x斜率为2, 二者相互垂直
OA和OB相互垂直
要使△PBD与△AOB全等, 只须PB = AO, PD = OB或PB = BO, PD = AO
∠ABO + ∠BAO = ∠BDP + ∠ABO = 90˚
所以∠BAO = ∠BDP, 只能PB = BO, PD = AO
OA = 2, OB = 1
y=2x沿x轴方向平移n个单位, 使△PBD与△AOB全等
直线变为y = 2(x - n)
C(n, 0), D(0, -2n)
y = 2(x - n)与y= - x/2 + 1联立, P((4n+2)/5, (4 - 2n)/5)
PB² = [(4n+2)/5 -0]² + [(4 - 2n)/5 - 1]² = (4n² + 4n + 1)/5 = 1
n² + n - 1 = 0
n = (-1 + √5)/2 (舍去(-1 - √5)/2 < 0)
直线平移 (-1 + √5)/2个单位
(2)
△PAC的面积 = (1/2)|AC|*|P的纵坐标| = (1/2)|2 - n|*|(4 - 2n)/5|
= (n - 2)²/5 = 4
n = 2 + 2√5 (舍去(2 - 2√5 < 0)