Question

Two distinct lines cannot have more than one point in common.
A) True
B) False

Answer 1

Hint: This statement can be proved using the method of contradiction. Assume that two distinct lines intersect at more than one point. Then we arrive at a contradiction.

Complete step-by-step answer:
We are asked to find out whether two distinct lines can have more than one point in common or not.
Let two lines $L_1$ and $L_2$ have more than one (say two) points in common.
Let it be $P$ and $Q$.
So we have two distinct lines passing through two distinct points $P$ and $Q$.
But this is a contradiction since we have the axiom that only one line can pass through two distinct lines.
So by method of contradiction, our assumption is wrong.
Two lines $L_1$ and $L_2$ cannot have more than one point in common.
Then the given statement is true.
Therefore the answer is option A.

Additional information:
A pair of lines can be called parallel, if they do not intersect. They are called perpendicular if the angle between them is ${90}^{\circ }$. In the coordinate system the two axes are considered as perpendicular to each other and the point of intersection is called the origin.

Note: Here we proved that two lines cannot intersect at more than one point. But it is not necessary that the lines intersect. If the lines are parallel, they do not intersect. In case of other lines, they intersect exactly at one point. In general, we can say that two lines intersect at most at one point.