Question

$x-y+6=0$, $2x+y-3=0$ and $x-2y+m=0$ are three lines. If these lines can form a triangle, then m cannot be .

• A. 10
• B. 11
• C. 12
• D. 13

Answer 1

The correct option is B 11

Three lines will form a triangle if they are not parallel and not concurrent.

The given lines are not parallel, since their slopes aren't equal. Now, if they are not concurrent, we can say they form a triangle.

Thus, the value of m for which the lines are concurrent is the value which m cannot take.

$x-y+6=0...\left(i\right)$

$2x+y-3=0...\left(ii\right)$

$\Rightarrow 3x+3=0$ from (i) and (ii)

$x=-1andy=5$

If (-1,5) lies on $x-2y+m=0$

$\Rightarrow -1-10+m=0$

$\Rightarrow m=11$

Thus, m cannot be 11