Question

How many line segments in all can be drawn between these points?

F) 4
G) 5
H) 6
J) 8​

Answer 1

6 line segments can be drawn

Answer 2

H) 6

Explanation:

You want to know the number of line segments that can be drawn between 4 noncollinear points.

Combinations

The number of possible segments is the number of unique pairs of points.

4 points can be chosen 2 at a time in (4·3/2) = 6 ways.

There are 6 possible line segments that can be drawn between these points.

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Additional comment

The number of combinations of k items from a field of n items is given by ...

nCk = n!/(k!(n-k)!)

For line segments, k=2, so this becomes (n)(n-1)/2.

The six (6) line segments are the four (4) around the outside to form a quadrilateral, and the two (2) across the middle that are the diagonals of that quadrilateral.

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