Question

If the point $(a,2)$ lies between the lines $x-y=1$ and $2x-2y+5=0,$ then the set of values of $a$ is

• A. $(-\infty ,3)\cup (\frac{9}{2},\infty )$
• B. $(\frac{-1}{2},3)$
• C. $(-\infty ,3)$
• D. $(3,\frac{9}{2})$

Answer 1

Answer: (B)

$(\frac{-1}{2},3)$

Given lines $x-y=1$ and $2x-2y+5=0$,they are parallel to each other.
As Point$(a,2)$ lies between lines ,we get $(a-2-1)\times (2a-4+5)<0⟹(a-3)(2a+1)<0$,

then $a$ lies in $(-\frac{1}{2},3).$