Q.
A rectangular billiard table has vertices at P0,0 , Q0,7, R10,7, and S10,0. A small billiard ball starts at M3,4moves in a straight line to the top M3,4, moves in a straight line to the top of the table, bounces to the right side of the table, and then comes to rest at N7,1. The y-coordinate of the point where it is the right side is
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a
3.7
b
3.8
c
3.9
d
4
answer is A.
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Detailed Solution
tanθ=a−13=7−a10−bAlso, tanθ=7−4b−3=3b−3Hence, 3b−3=a−13=7−a10−bFrom the first two relations, we have 9=ab−b−3a+3or 3a+6=ab−b (1)From the last two relations, we have 10a−ab−10+b=21−3aor 13a−ab+b=31or ab−a=13a−31 (2 )Hence, from (1) and (2),3a+6=13a−31or 10a=37or a=3.7
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