Question

How many lines can be drawn that pass through two different lines?
A. 1
B. 2
C. 3
D. Infinite

Answer 1

Hint: Here we use Euclid’s first postulate to find the number of lines that can be drawn that pass through two different lines.
* Euclid’s First Postulate: A straight line segment can be drawn joining any two points.
* Line: A line is a straight one dimensional figure that extends infinitely on both sides. So a line has no fixed end points.

Complete step-by-step solution:
We know if one point is fixed we can draw an infinite number of lines through that one single point.
Let us draw lines that can be drawn through one point. Let us consider a single fixed point as O.

But here we are given there are two different points.
If we look separately at each point, there are infinite numbers of lines that can be drawn through each point. If we take two distinct points A and B, then the figure drawn below shows us the number of lines each point can have if taken individually.

But if we try to draw a line that passes through both the points, then we can draw only one line that passes through both the different points.

AB is the only single straight line that passes through both the points.
So, the number of lines that can be drawn that pass through two different points is 1.

\[\therefore \]Correct option is A.

Note: Students might choose the wrong option as B (2) as they might think one line is from left point A to B and other line is from point B to A. Keep in mind if we write line AB then it is same as line BA. Many students try to draw curved lines that join point s AB, but this is unacceptable here as we need a straight line not curved line.