Question

State whether the following sentences are true or false also give reasons for your answer
1 two distinct lines can have more than one point in common
2 only one line can pass through a given point

Answer 1

Answer:

(a) False

(b) False

Step-by-step explanation:

(a) two distinct points will always Join at one point hence there can't be more than one point in common

(b) Infinite number of lines can pass through a given point

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Answer 2

Two distinct lines can have more than one point in common ⇒ false

Only one line can pass through a given point ⇒ false

Solution:

Given, two statements are  

1. Two distinct lines can have more than one point in common  

2. only one line can pass through a given point

We have to state whether the following sentences are true or false also give reasons for your answer  

Now, take 1) two distinct lines can have more than one point in common  

No, that’s not possible, a point in common means that it is an solution to the system of equations and in order have to more than 1 solution the lines should be dependent which means same lines, but here we are given that lines are distinct. So that’s not possible. It will be possible in case of curves but not possible in case of lines.

Now, take 2) only one line can pass through a given point

No, even this is not possible, because we know many lines pass through a point at different slopes, and they all are called family of lines. So this is wrong statement.

Hence, none of the given statements are correct

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