Which of the following statements is false?a)A line can be produced to any desired length.b)Through a given point, only one straight line can be drawn.c)Through two given points, it is possible to draw one and only one straight lined)Two straight lines can intersect in only one pointCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

The correct option is Option B.

Infinite number of lines can pass through one point.

Answer

Hi!

Infinite lines can be drawn through a single point. This is an axiom (a statement that can be taken for granted).

Answer

Through a given point, only one straight line can be drawn.

This statement is false.

Explanation:

1. A line can be produced to any desired length

A line can be extended indefinitely in both directions. This means that a line can be produced to any desired length. Therefore, this statement is true.

2. Through a given point, only one straight line can be drawn

This statement is false. Through a given point, an infinite number of straight lines can be drawn. This is because a straight line can be drawn in any direction from a given point. For example, if we consider a point on a piece of paper, we can draw a straight line from that point in any direction - up, down, left, right, or at any angle. Therefore, there are multiple straight lines that can be drawn through a given point.

3. Through two given points, it is possible to draw one and only one straight line

This statement is true. Given two points, there is only one straight line that can pass through both of them. This is known as the unique line property. No matter how close or far apart the two points are, there will always be exactly one straight line connecting them.

4. Two straight lines can intersect in only one point

This statement is true. If two straight lines intersect, they can only intersect at one point. This is known as the intersection property. If two lines were to intersect at more than one point, they would no longer be considered straight lines. Therefore, two straight lines can intersect in only one point.

In conclusion, the false statement among the given options is 'Through a given point, only one straight line can be drawn.' As explained above, through a given point, an infinite number of straight lines can be drawn.

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