Questions & Answers

How many lines can pass through a given point?
(a) 1
(b) 2
(c) 3
(d) Infinitely many

Answer Verified Verified
Hint: To count the number of lines passing through a fixed point in the plane, try to draw lines in all possible directions which pass through a fixed point. Consider all the possible slopes of lines. Count the number of lines which are passing through the point.

Complete step-by-step answer:

We have to find the number of lines that pass through a given point.
Let us consider a fixed point P in the plane. We have to count the number of lines passing through this point. We will try to draw all possible lines passing through the point at all possible slopes.

We can draw lines in multiple directions with multiple slopes. Thus, we observe that we can draw lines with all possible real values of slopes.
As the set of real numbers is of infinite size, we can draw an infinite number of lines passing through a fixed point.
Hence, through any point in the plane, we can draw infinite lines passing through the point, which is option (d).

Note: We need to clearly know the definition of a point and a line. A point is an exact position or a location in the plane. Point is considered as a dimensionless object in the plane. While, a line is defined as a one dimensional figure that has no thickness and can be extended endlessly in both directions. A line doesn’t have a starting or an ending point. It is just endless. It is not practically possible to count all the lines passing through a point. Thus, we count the number of lines based on the number of possible slopes of the lines.
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