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Maths Straight Line Mix Single Correct MCQ

Published on: August 14, 2026

If P is a point (x, y) on the line y = – 3x such that P & the point (3, 4) are on the opposite sides of the line 3x – 4y = 8; then :

x> 8/15, y < – 8/5

x > 8/5, y < – 8/15

x = 8/15, y = – 8/5

None of these

Text Solution

Verified by Experts

The correct answer is:

Let k = 3x – 4y – 8

then value of k at (3,4)

= 3 × 3 – 4 × 4 – 8 = – 15 < 0

∴ For point P(x, y) we should have k > 0

⇒ 3x – 4y – 8 > 0

⇒ 3x – 4(– 3x) – 8 > 0{ P(x,y)lie on y = –3x}

⇒ 15x – 8 > 0 ⇒ x > 8/15

and – y – 4y – 8 > 0

y < – 8/5

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