Right triangle PQR is to be constructed in the xy-plane so t

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/06/30 19:57:46

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis.The x-and y-coordinates of P,Q,and R are to be integers that satisfy the inequalities -4≤x≤5,6≤y≤16.How many different triangles with these properties could be constructed?
(A)110 (B)1100 (C)9900 (D)10000 (E)12100

选择C.将可能的所有点描出来,是一个10*11的矩形.因为高不能为0且PR平行于x轴,p是直角点,因此我们首先定PR边.在同一个y坐标下PR只需从10个点里任取2点就行,共有10*9/2=45种可能（排列与组合中的组合）然后定高,高就是那11点里除PR边所在的那一条线的其它10点里任选,所以有45*10=450种.而PR纵坐标的选择有11种,所以有450*11=4950种.最后P点是再PR里任选一个,所以一共有4950*2=9900种三角形.

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