Question

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

• A. $7<a<11$
• B. $a=7$
• C. $a=11$
• D. $a<7ora>11$

Answer 1

Answer: (A)

$7<a<11$

If the two points are $(1,2)$ & $(3,4)$ are opposite to line $3x-5y+a=0$ then,
$(3\times (1)-5\times (2)+a)(3\times 3-5\times 4+a)<0$

$\Rightarrow (a-7)(a-11)<0$
$\Rightarrow 7<a<11$
Hence, option 'A' is correct.