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     

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If P is a point (xy) 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   



Correct option is

x > 8/15, y < – 8/5

Let k = 3x – 4y – 8

Then the value of k at (3, 4) = 3 × 3 – 4 × 4 – 8 = –15 < 0  

∴ For the point P (xy) we should have k > 0

⇒ 3x – 4y – 8 > 0    

⇒ 3x – 4(–3x) – 8 > 0 [∵ P (xy) lies on y = –3x

⇒ x > 8/15   

and   –y – 4y – 8 > 0 ⇒ y < –8/5. 



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