Question

In how many points can two distinct lines at most intersect?
$(a)$ Only one
$(b)$ Only two
$(c)$ Only 3
$(d)$ Infinitely many

Answer 1

Hint – Intersection means that the point which satisfies both the equations of the lines. Use this concept to think of the total points at which two lines can interest.

Complete step-by-step answer:

Let us consider two lines (A) and (B) which are distinct to each other.

i.e. The slopes of the lines are different; they are not parallel to each other.

So if A and B are not parallel to each other then they will intersect at a single point otherwise they will not intersect.

Hence two distinct lines can intersect at most at one point as shown in figure.

So this is the required answer.

Hence option (a) is correct.

Note – There can be misconception regarding this question that two distinct lines can have infinitely many points of intersection as if we have two lines overlapping each other then? But we need to understand overlapping doesn’t mean intersecting as they are simply parallel with a perpendicular distance between them being very small.