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 and 6 <= y <= 16. How many different triangles with these properties could be constructed?
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100
There has to be a relatively easy way to solve this. Please post your answer and explanation. What makes this difficult for me at least is that it involves elementary combinatorics in addition to simple coordinate geometry.
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100
There has to be a relatively easy way to solve this. Please post your answer and explanation. What makes this difficult for me at least is that it involves elementary combinatorics in addition to simple coordinate geometry.
