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If P is a point (x ,y) on the line y=-3x...

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)`

A

`x gt 8//15`

B

`x gt 8//5`

C

`x lt -8//5`

D

`y lt -8//15`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Let L=3x-4y-8. Then the value of L at (3,4) is `3 xx 3-4 xx 4-8 = -15 lt 0.` Hence, for the point P(x,y), we should have
`L lt 0`
`"or " 3x-4y-8 gt 0`
`"or " 3x-4(-3x)-8 gt 0 " " [because P(x,y) " lies on "y = -3x]`
`"or " x gt (8)/(15)`
`"and " -y-4y-8 gt 0`
`"or " y lt -(8)/(5)`
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Knowledge Check

  • If the points (1,2) and (3, 4) are on the opposite side of the line 3x - 5y + a = 0, then :

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    B
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    (1,4)
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  • The distance of the line 2x-3y=4 from the point (1,1) in the direction of the line x+y=1 is

    A
    `sqrt2`
    B
    `5sqrt2`
    C
    `1/sqrt2`
    D
    none of these

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