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【简答题】
如图,点B 1 (1,y 1 ),B 2 (2,y 2 ),B 3 (3,y 3 )…,B n (n,y n )(n是正整数)依次为一次函数 的图象上的点,点A 1 (x 1 ,0),A 2 (x 2 ,0),A 3 (x 3 ,0),…,A n (x n ,0)(n是正整数)依次是x轴正半轴上的点,已知x 1 =a(0<a<1),△A 1 B 1 A 2 ,△A 2 B 2 A 3 ,△A 3 B 3 A 4 …△A n B n A n+1 分别是以B 1 ,B 2 ,B 3 ,…,B n 为顶点的等腰三角形。 (1)写出B 2 ,B n 两点的坐标; (2)求x 2 ,x 3 (用含a的代数式表示);分析图形中各等腰三角形底边长度之间的关系,写出你认为成立的两个结论; (3)当a(0<a<1)变化时,在上述所有的等腰三角形中,是否存在直角三角形?若存在,求出相应的a的值;若不存在,请说明理由。
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