We are learning about proofs. We drew lines between noncollinear points. Our table showed 2 points >> 1 line segment, 3 point >> 3 line segments, 4 points >> 6 line segments, 5 points >> 10 line seg, 6 points >> 15 line seg. etc.

Write an expression in terms of n for the number of line segments that can be drawn between n points.

Please help.

1, 3, 6, 10,.. is the series

N*(N-1)/2
where N is the number of points.

These are sometimes refered to as triangle numbers. (This of stacking pop cans in a triangle with rows of 1, 2, 3, 4 etc.)

See http://en.wikipedia.org/wiki/Triangular_numbers

Thank you very much. I could explain it (I thought) but couldn't express it in math terms. Thanks again

line segment 6cm and divide 5 congruent parts

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

To find an expression in terms of n for the number of line segments that can be drawn between n points, you can observe the pattern in your table.

It appears that the number of line segments increases by 1 each time you add a point. Additionally, each new point can potentially form a line segment with every previous point (excluding itself and any points in the same line).

Let's break down the pattern:

- With 2 points, you can draw 1 line segment.
- With 3 points, you can draw 2 additional line segments, making a total of 3.
- With 4 points, you can draw 3 more line segments, making a total of 6.
- With 5 points, you can draw 4 more line segments, making a total of 10.
- With 6 points, you can draw 5 more line segments, making a total of 15.

Do you notice any patterns or relationships?

If you take the number of points (n) and subtract 1 (to account for the line segment connecting each point to itself), you will get the number of line segments that each point can potentially form.

For example, with 6 points, each point can potentially form 6 - 1 = 5 line segments. This holds true for all the examples in your table.

However, we need to account for the fact that every time a new point is added, it can form line segments not only with the previous points but also with the new point itself.

So, to find the total number of line segments, you can calculate the sum of the number of line segments each point can potentially form (n - 1) and add 1 more for each additional point.

In mathematical terms, the expression for the number of line segments that can be drawn between n points is:
(n-1) + (n-2) + (n-3) + ... + 2 + 1

This is equivalent to the sum of the first (n-1) positive integers, which can be represented using a formula:

n*(n-1)/2

Thus, the expression for the number of line segments that can be drawn between n points is n*(n-1)/2.

You can simplify this expression further if needed.