Question

中，，，cm．長為1cm的線段在的邊上沿方向以1cm/s的速度向點運動（運動前點與點重合）．過分別作的垂線交直角邊于兩點，線段運動的時間為s．

（1）若的面積為，寫出與的函數關系式（寫出自變量的取值范圍）；

（2）線段運動過程中，四邊形有可能成為矩形嗎？若有可能，求出此時的值；若不可能，說明理由；

（3）為何值時，以為頂點的三角形與相似？

Answer 1

解：（1）當點在上時，，．

．········································································ 2分

當點在上時，．

．·················································· 4分

（2），．．

．········································································ 6分

由條件知，若四邊形為矩形，需，即，

．

當s時，四邊形為矩形．································································ 8分

（3）由（2）知，當s時，四邊形為矩形，此時，

．··························································································· 9分

除此之外，當時，，此時．

，．．····························· 10分

，．

又，．········································ 11分

，．

當s或s時，以為頂點的三角形與相似．·················· 12分