A rectangular billiard table has vertices at P(0, 0),Q(0 ,7),R( 10,7), and ,S( 10, 0). A small billiard ball starts at M(3, 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 ,N(7, 1). The /-coordinate of the point where it hits the right side is

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3.8

3.7

3.9

answer is A.

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Detailed Solution

$\tan θ = \frac{a - 1}{3} = \frac{7 - a}{10 - b}$
Also, $\tan θ = \frac{7 - 4}{b - 3} = \frac{3}{b - 3}$

Hence, $\frac{3}{b - 3} = \frac{a - 1}{3} = \frac{7 - a}{10 - b}$
From the first two relations, we have
or $3 a + 6 = ab - b$ ………………………………….(1)
From the last two relations, we have
$10 a - ab - 10 + b = 21 - 3 a$
or $13 a - ab + b = 31$
or $ab - b = 13 a - 31$ …………………………………(2)
Hence, from (1) and (2),
$3 a + 6 = 13 a - 31$
or $10 a = 37$
or $a = 3 .7$