Question
Question: If P is a point (x, y) on the line y = – 3x such that P & the point (3, 4) are on the opposite sides...
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 :
A
x> 8/15, y < – 8/5
B
x > 8/5, y < – 8/15
C
x = 8/15, y = – 8/5
D
None of these
Answer
x> 8/15, y < – 8/5
Explanation
Solution
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
Ž 3x – 4y – 8 > 0
Ž 3x – 4(– 3x) – 8 > 0{
P(x,y)lie on y = –3x}
Ž 15x – 8 > 0 Ž x > 8/15
and – y – 4y – 8 > 0
y < – 8/5