解(1):过点A(1,2),B(1,3)的直线垂直于x轴,直线AB的斜率不存在,AB与y轴的距离为1,AB的直线方程为x=1
(2):设所求直线的倾斜角为θ,直线y=(1/2)x+1的倾斜角的正切值为1/2
根据题意tanθ/2=1/2
tanθ=(2tanθ/2)/(1-tan²/θ/2)
=(2×1/2)/[1-(1/2)²]
=1/(3/4)
=4/3
过点A(1,2),倾斜角是直线y=(1/2)x+1的倾斜角的两倍的直线方程为:
y-2=(4/3)(x-1)
化成一般式为(4/3)x-y-2/3=0