Question

If the points $(1,2)$ and $(3,4)$ lie on the same side of the straight line $3x-5y+a=0$ then a lies in the set

• A. $[7,11]$
• B. $R-[7,11]$
• C. $[7,\infty )$
• D. $(-\infty ,11]$

Answer 1

Answer: (B)

$R-[7,11]$

Since $(1,2)$ and $(3,4)$ lie on the same side of the line,

$3\left(1\right)-5\left(2\right)+a$ and $3\left(3\right)-5\left(4\right)+a$ must have the same sign.

Hence $(3-10+a)(9-20+a)>0$

or $(a-7)(a-11)>0$

For $a$ in $[7,11]$ the above expression becomes negative.

Hence a lies in the set $R-[7,11]$.