Re: [請教] M3的數學一題
※ 引述《pklapkla (被發現了＞＜)》之銘言：
: Right triangle PQR is to be constructed in the XY-plane so that 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 and 6<=Y<=16.
: How many different triangles with these properties could be constructed?
: (A) 100
: (B) 1100
: (C) 9900
: (D)10000
: (E)12100
: 答案C
: 想請問題目如何解釋??還有如何算出答案??
: 感激不盡^^~~
直角三角形PQR，直角在P，PR和X軸平行
-4<=X<=5 and 6<=Y<=16
所以PR就是在-4<=X<=5中任意取兩點 C(10 2)
還要考慮PR可以垂直移動 C(11 1)
所以PR共有C(10 2)*C(11 1)
高PQ就是在6<=Y<=16中任意取一點 C(10 1)
然後不要忘記了PQ和QP的情況，會造成Q點有兩種情況
所以要在成2
所以C(10 2)*C(11 1)*C(10 1)*2=9900
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