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 $M (3, 4),$ 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 y-coordinate of the point where it is the right side is

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Infinity Learn · Accepted Answer

$$tan$$θ$$=a$$−$$13=7$$−$$a10$$−bAlso, $$tan$$θ$$=7$$−$$4b$$−$$3=3b$$−$$3Hence$$, $$3b$$−$$3=a$$−$$13=7$$−$$a10$$−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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