If `P` is a point `(x ,y)` on the line `y=-3x` such that `P` and the point (3, 4) are on the opposite sides of the line `3x-4y=8,` then `x >8/(15)` (b) `x >8/5` `y<-8/5` (d) `y<-8/(15)`

Options

A. `x gt (8)/(15),y lt -(8)/(5)`
B. `x gt (8)/(5), y lt -(8)/(15)`
C. `x=(8)/(15),y=-(8)/(5)`
D. None of these

Answer

A

Explanation

Let `L_(1)-=3x-4y-8=0`
At point (3,4).
`L_(1)-=9-16-8=-15lt0`
As point (x,y) and (3,4) opposite sides of `L_(1)`.
`therefore3x-4y-8 gt 0` . . . (i)
`implies3x-4(-3x)-8gt0" "[becausey=-3x]`
`implies15x-8gt0impliesxgt(8)/(15)`
Again from Eqn. (i),
`3(-(y)/(3))-4y-8gt0`
`implies-5y-8gt0impliesylt-(8)/(5)`