如图，矩形ABCD的边分别与两坐标轴平行，对角线AC经过坐标原点，点D在反比例函数（x＞0）的图象上．若点B的...

问题详情：

如图，矩形ABCD的边分别与两坐标轴平行，对角线AC经过坐标原点，点D在反比例函数（x＞0）的图象上．若点B的坐标为（﹣4，﹣4），则k的值为（　　）                                  

A．2                            B．6                            C．2或3                       D．﹣1或6

【回答】

D【考点】反比例函数综合题．                                                               

【专题】计算题．                                                                              

【分析】根据矩形的对角线将矩形分成面积相等的两个直角三角形，找到图中的所有矩形及相等的三角形，即可推出S四边形DEOH=S四边形FBGO，根据反比例函数比例系数的几何意义即可求出k2﹣5k+10=16，再解出k的值即可．                

【解答】解：如图：                                                                          

∵四边形ABCD、FAEO、OEDH、GOHC为矩形，                                           

又∵AO为四边形FAEO的对角线，OC为四边形OGCH的对角线，                    

∴S△AEO=S△AFO，S△OHC=S△OGC，S△DAC=S△BCA，                                        

∴S△DAC ﹣S△AEO﹣S△OHC=S△BAC﹣S△AFO﹣S△OGC，                                    

∴S四边形FBGO=S四边形DEOH=（﹣4）×（﹣4）=16，                                              

∴xy=k2﹣5k+10=16，                                                                        

解得k=﹣1或k=6．                                                                             

故选：D．                                                                                         

知识点：反比例函数

题型：选择题