过点A(-1,1)作直线l,使它被两平行线l1:x+2y-1=0和:x+2y-3=3所截得线段的中点恰好在直线l3:x-y-1=0上,求直线l的方程
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![过点A(-1,1)作直线l,使它被两平行线l1:x+2y-1=0和:x+2y-3=3所截得线段的中点恰好在直线l3:x-y-1=0上,求直线l的方程](/uploads/image/z/4346227-19-7.jpg?t=%E8%BF%87%E7%82%B9A%28-1%2C1%29%E4%BD%9C%E7%9B%B4%E7%BA%BFl%2C%E4%BD%BF%E5%AE%83%E8%A2%AB%E4%B8%A4%E5%B9%B3%E8%A1%8C%E7%BA%BFl1%EF%BC%9Ax%2B2y-1%3D0%E5%92%8C%EF%BC%9Ax%2B2y-3%3D3%E6%89%80%E6%88%AA%E5%BE%97%E7%BA%BF%E6%AE%B5%E7%9A%84%E4%B8%AD%E7%82%B9%E6%81%B0%E5%A5%BD%E5%9C%A8%E7%9B%B4%E7%BA%BFl3%EF%BC%9Ax-y-1%3D0%E4%B8%8A%2C%E6%B1%82%E7%9B%B4%E7%BA%BFl%E7%9A%84%E6%96%B9%E7%A8%8B)
过点A(-1,1)作直线l,使它被两平行线l1:x+2y-1=0和:x+2y-3=3所截得线段的中点恰好在直线l3:x-y-1=0上,求直线l的方程
过点A(-1,1)作直线l,使它被两平行线l1:x+2y-1=0和:x+2y-3=3所截得线段的中点恰好在直线l3:x-y-1=0上,
求直线l的方程
过点A(-1,1)作直线l,使它被两平行线l1:x+2y-1=0和:x+2y-3=3所截得线段的中点恰好在直线l3:x-y-1=0上,求直线l的方程
中点在直线x-y-1=0上,满足y=x-1
设该中点为(x0,x0-1)
该中点到两条平行线的距离相等
|x0+2(x0-1)-1|/√(1+4)=|x0+2(x0-1)-6|/√(1+4)
|3x0-3|=|3x0-8|
3x0-3=8-3x0
x0=11/6
所以,中点为(11/6,5/6)
直线l斜率=(5/6-1)/(11/6+1)=-1/17
直线l方程:y-1=(-1/17)(x+1)
即,x+17y-16=0
l:y-1=k(x+1)
y=k(x+1)+1
x+2y-1=0
x+2y-3=0
x+2(k(x+1)+1)-1=0
x+2kx+2k+2-1=0
x1=-(1+2k)/(1+2k)
x2=(1-2k)/(1+2k)
x=1/2(x1+x2)=1/2*(-4k)/(1+2k)=-2k/(1+2k)
y=x-1=-2k/(1+...
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l:y-1=k(x+1)
y=k(x+1)+1
x+2y-1=0
x+2y-3=0
x+2(k(x+1)+1)-1=0
x+2kx+2k+2-1=0
x1=-(1+2k)/(1+2k)
x2=(1-2k)/(1+2k)
x=1/2(x1+x2)=1/2*(-4k)/(1+2k)=-2k/(1+2k)
y=x-1=-2k/(1+2k)-1=-(1+4k)/(1+2k)
-(1+4k)/(1+2k)=k(-2k/(1+2k)+1)+1
-1-4k=-2k^2+(k+1)(1+2k)
-1-4k=-2k^2+2k^2+3k+1
7k=-2
k=-2/7
y-1=-2/7(x+1)
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