$解：?(1)?∵點?E?是對角線?BD?的中點$
$又∵四邊形?ABCD?是矩形$
$∴點?E?是?AC?的中點$
$∵點?E?的縱坐標為?m?$
$∴點?A?的縱坐標為?2m?$
$?(2)?∵?∠ABD=45°?$
$∴?AD=AB=2m?$
$∵點?A?在函數?y=\frac 3 x?的圖像上，且點?A?的縱坐標為?2m?$
$∴?A(\frac 3 {2m}，??2m)?$
$∴?B(\frac 3 {2m}，??0)，??D(\frac 3{2m}+2m，??2m)?$
$∵?E?是?BD?的中點$
$∴?E(\frac 3 {2m}+m，??m)?$
$∵?E?在函數?y=\frac 3 x?的圖像上$
$∴?m(\frac 3 {2m}+m)=3?$
$解得，?m=\frac {\sqrt {6}}2(?負值舍去)$
$∴?m?的值為?\frac {\sqrt {6}}2?$
