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Question

If the points $$\displaystyle \left ( 1,2 \right )$$ and $$\displaystyle \left ( 3,4 \right )$$ were to be on the opposite side of the line $$\displaystyle 3x-5y+a=0$$, then


A
7<a<11
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B
a=7
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C
a=11
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D
a<7ora>11
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Solution

The correct option is B $$\displaystyle 7< a< 11$$
If the two points are $$(1,2)$$ & $$(3,4)$$ are opposite to line $$3x-5y+a=0 $$ then,
$$(3\times(1)-5\times(2)+a)(3\times3-5\times4+a)<0  $$
$$\Rightarrow (a-7)(a-11) <0$$
$$\Rightarrow 7<a<11$$
Hence, option 'A' is correct.

Mathematics

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