問數~10fun

1)
L,:2ax-3y+1=0的斜率=-2a/(-3)=2a/3
L,,:y=1-3ax的斜率=-3a

兩直線互相垂直,它們的斜率的乘積=-1
(2a/3)(-3a)=-1
-2a^2=-1
a^2=1/2
a=±√(1/2)

2)
L,:y=x的斜率=1
L,,:(k+2)x+(k+1)y-1=0的斜率=-(k+2)/(k+1)

兩直線互相平衡,它們的斜率相等
-(k+2)/(k+1)=1
-(k+2)=k+1
-k-2=k+1
2k=-3
k=-3/2

3)
AB斜率=(-3-3)/(6-2)=-3/2
AB中點=[(6+2)/2,(-3+3)/2]=(4,0)

所以垂直平分線方程:
y-0=[-1/(-3/2)]*(x-4)
y=2(x-4)/3
3y=2x-8
2x-3y-8=0