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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

  • The image of the point (3, 8) with respect to the line x + 3y = 8 is

    A
    (5, `(-17)/(4)`)
    B
    (`(-5)/(4)`, -4)
    C
    (0, -1)
    D
    None of these

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