Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Let y = mx + c be the line through points (-1, 2).

2 = m (-1) + c

⇒ c = m + 2

Thus, y = mx + m + 2 --------------- (1)

The given line as

x + y = 4 ------------ (2)

On solving these equations, we get,

and

Thus, is the point of intersection of lines (1) and (2).

Since, this point is at a distance of 3 units from point (-1, 2),

So, now using distance formula,

⇒ 1 + m² = m² + 1 + 2m

⇒ 2m = 0

⇒ m = 0

Therefore, the slope of the required line must be zero,

Hence, the line must be parallel to the x – axis.