Question

# Given 6 collinear points, make a conjecture about the number of ways to connect different pairs of points.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

## The correct answer is: Hence, the conjecture that can be concluded is “the number of ways to connect the 6 collinear points in different pairs of points is 15”.

### Let’s first make a table and then look for the pattern

The sequence of the number of connections is 0, 1, 3, 6, 10, ….

We can see that

1 = 0 + 1

3 = 1 + 2

6 = 3 + 3

10 = 6 + 4

So by seeing the pattern the number of connections in 6 points is given as

10 + 5 = 15

So by seeing the pattern the conjecture that can be made is that the number of ways to connect the 6 collinear points in different pairs of points is 15

Final Answer:

Hence, the conjecture that can be concluded is “the number of ways to connect the 6 collinear points in different pairs of points is 15”.

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