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Question

If P(x,y) is a point on the line y=3x such that P and Q(3,4) are on opposite side of the line 3x4y=8, then

A
x>85,y<815
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B
x>815,y<85
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C
x=815,y=85
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D
x=2,y=2
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Solution

The correct option is B x>815,y<85
Let k=3x4y8
then the value of k at (3,4)=3×34×48=15<0
For the point P(x,y) we should have k>0
3x4y8>0
3x4(3x)8>0 [P(x,y) lies on y=3x]
x>815
and y4y8>0y<85.

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