OG-11 PS 248

[Sankofi]

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

Please explain

OA is C

[stop@800]

One point can be chosen in 11 ways
another in 10 ways and last one in 9 ways

so 11*10*9
9900

[aj5105]

can you elaborate ur answer a bit more?

[mental]

One point can be chosen in 11 ways
another in 10 ways and last one in 9 ways

so 11*10*9
9900

STOP: i suppose there was a typo
11*10*9 = 990

neways, you must have meant (11*10)*(10*9)

y can have 11 integral co-ordinates, out of that two can be chosen in 11*10 ways

x can have 10 integral co-ordinates, so two can be chosen in 10*9 ways

so total triangles = 11*10*10*9 = 9900

THIS QUESTION CAN BE FOUND IN EARLIER POSTS

[Sankofi]

Thanks. I did a search and was not able to find, sorry.