A rectangular billiard table has vertices at `P(0,0),Q(0,7),R(10 ,7),` and `S(10 ,0)dot` 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 `y-` coordinate of the point where it hits the right side is 3.7 (b) 3.8 (c) 3.9 (d) 4

Options

A. `3.7`
B. `3.8`
C. `3.9`
D. 4

Answer

A

Explanation

`tantheta=(a-1)/(3)=(7-a)/(10-b)`
Also, `tantheta=(7-4)/(b-3)=(3)/(b-3)`

Hence, `(3)/(b-3)=(a-1)/(3)=(7-a)/(10-b)`
From the first two relations, we have
`9=ab-b-3a+3`
or `3a+6=ab-b`
From the last two relations, we have
`10a-ab-10+b=21-3a`
or `3a-ab+b=31`
or `ab-b=13a-31`
Hence, from (1) and (2) ,
`3a+6=13a-31`
or `10a-37`
or `a=3.7`