you can draw one segment to connect two points and three distinct segments to connect three named points. how many segments can you drawto connect five points if no three of the points lie on the same line.........please help me i am confused
To solve this problem, we can use the formula for the number of segments that can be drawn to connect n points, where no three points lie on the same line.
Let's break this down step by step:
1. Start with the given information:
- You can draw one segment to connect two points.
- You can draw three distinct segments to connect three named points.
2. Based on the given information, we can conclude that the number of segments we can draw to connect four points is two, since no three points lie on the same line.
3. Now, let's consider the case of connecting five points. We have four points already connected using two segments.
4. To connect the fifth point with the other four points, we need to draw a segment that connects it with each of the other points. However, we need to make sure that no three points lie on the same line.
5. Since no three points lie on the same line, we can draw three distinct segments to connect the fifth point with the other four points, similar to the initial case of connecting three points.
6. Therefore, to connect five points, we would need a total of two segments (connecting the first four points) plus three distinct segments (connecting the fifth point with the other four points).
Thus, the total number of segments that can be drawn to connect five points, where no three points lie on the same line, is five.