请教一道og12 数学题（ps 229 题）

beccayule

请教您下面这道题。og解释看不太懂，谁讲解提示下。感谢

og 12 problem solving 229题：

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-coordinate of p, q, and r are to be integer that satisfy the inequalities -4<=X<=5 and 6<=Y<=16. How many different triangles with these properties could be constructed?

A. 110
B. 1100
C. 9900
D. 10000
E. 12100

vivianwei700

可以确定X轴上10个点，Y轴上11个点，满足要求的三角形为：P(10，2)*P(11，2) 排列公式。即：10*9*11*10=9900

fxj25860

首先，可以判断 P R 两点纵坐标一样，横坐标可以从横轴的10个点中任选两点进行排列，其次，Q P 两点的横坐标一致，纵坐标可以从纵轴的11个点中任选两点排列，因而最后应该是 A 10 2* A 11 2=10*9*11*10=9900