如图,A（0,4）B（3,0）C（4,2）,且反比例函数图象经过点C

(1) A(0,4) B(3,0) C(4。2) D(x1,y1)|AB|=√((0-3)^2+(4-0)^2)=5kAB=(4-0)/(0-3)=-4/3平行四边形：|CD|=|AB| kCD=kAB√((x1-4)^2+(y1-2)^2)=5(x1-4)^2+(y1-2)^2=25。(1)(y1-2)/(x1-4)=-4/3y1-2=-4/3(x1-4)。(2)(2)代入(1)：(x1-4)^2+(-4/3(x1-4))^2=25(x1-4)^2(1+16/9)=25(x1-4)^2=9x1-4=±3x1=4+3=7y1-2=-4/3(7-4)y1=-2或者x1=4-3=1y1-2=-4/3(1-4)y1=6D(7,-2)或者D(1,6)(2) C(4,2)在y=k/x上2=k/4k=8y=8/x设Q(q,8/q)到AB的距离为d (q>0)AB方程：(y-0)/(x-3)=(4-0)/(0-3)4x+3y+12=0d=|4q+3*8/q+12|/√(4^2+3^2)=4|q+6/q+3|/5SΔABQ=1/2|AB|*4|q+6/q+3|/5=2/5*5|q+6/q+3|=2|q+6/q+3|q+6/q>=2√q*√(6/q)=2√6当q=6/q时,q+6/q有最小值：2√6SΔABQmin=2|2√6+3|=4√6+6(2) 解法2：C(4,2)在y=k/x上2=k/4k=8y=8/x当y=8/x上某点的切线与AB平行时,三角形ABQ的面积最小。y'=-8/x^2=kAB=-4/3x^2=6x=±√6(∵在第一象限,∴x=√6)y=8/√6=4√6/3Q(√6,4√6/3)AB方程：(y-0)/(x-3)=(4-0)/(0-3)4x+3y+12=0Q到AB的距离：d=|4*√6+3*4√6/3+12|/√(4^2+3^2)=(8√6+12)/5SΔABQmin=1/2*|AB|*d=1/2*5*(8√6+12)/5=4√6+6