Question

The vertices of a $\Delta OBC$ are O(0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is $\frac{1}{2}$, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The equation of line BC is x + y + 4 = 0
$\therefore$ Equation of a line parallel to BC is x + y + k = 0
This is at a distance $\frac{1}{2}$ from the origin

$\therefore \left|\frac{k}{\sqrt{2}}\right|=\frac{1}{2}\therefore k=\pm \frac{1}{\sqrt{2}}$
Since BC and the required line are on the same side of the origin
$\therefore k=\frac{1}{\sqrt{2}},theequationisx+y+\frac{1}{\sqrt{2}}=0$