P and C

Question

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P
and line 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 :– $-4\leq x \leq 5$ and $6\leq y \leq 16$ . How many different triangles could be
constructed with these properties ?
(a) 110 (b) 1,100 (c) 9,900 (d) 10,000

Comments

9900??

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given ans is 1100, tell me how you did ?

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is it C)??

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−4≤x≤5 (10 values)

6≤y≤16(11 values)

for P to choose it's coordinate we have ₁₀C₁ * ¹¹C_{1  =110}

For R (PR is parallel to X axis means Y coordinate of them is same) =⁹C₁   Bcz it can't have x cor equal to x cor of P

For Q (it's x cor is same as that of P) =¹⁰C₁(for y corr and it is not 11c1 bcz they will fall in same line)

Total=110*9*10=9900