There are ten straight lines in a plane, no two of which is parallel, and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is :a)720b)630c)365d)noneCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

10 straight line no two of which is parallel and no three pass through the same point⇒ points =

Answer

10 straight line no two of which is parallel and no three pass through the same point⇒ points =

Answer

The given problem involves ten straight lines in a plane, with no two lines being parallel and no three lines passing through the same point. We need to determine the number of fresh lines that are obtained by joining the points of intersection.

Let's analyze the problem step by step:

1. Intersection Points:
When two lines intersect, they create one intersection point. The number of intersection points can be found using the formula nC2, where n represents the number of lines. In this case, we have ten lines, so the number of intersection points is 10C2 = 45.

2. Intersection Lines:
Each intersection point can be joined to every other intersection point, excluding those points that lie on the same line. To find the number of intersection lines, we use the formula nC2 - n, where n represents the number of intersection points. In this case, we have 45 intersection points, so the number of intersection lines is 45C2 - 45 = 990 - 45 = 945.

3. Fresh Lines:
Now, we want to find the number of fresh lines that are obtained by joining the points of intersection. These fresh lines are formed by connecting any two intersection points that do not lie on the same line. As no three lines pass through the same point, each fresh line will be unique.

To determine the number of fresh lines, we need to subtract the number of intersection lines from the total number of lines formed by joining the intersection points. Therefore, the number of fresh lines is 45 - 945 = -900.

Since the result is negative, it implies that there are no fresh lines obtained by joining the points of intersection.

Hence, the correct answer is option D) none.

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