21 line segments are needed to connect each dot to each other dot.
Since, there are 7 dots on a piece of paper such that no 3 dots are in a straight line.
We know that a line segment has two endpoints.
Number of line segments formed by n points = [tex]\dfrac{n(n-1)}{2}[/tex]
So the required number of line segments are needed to connect given 7 dots (each dot to each other dot
)[tex]=\dfrac{7(7-1)}{2}[/tex]
[tex]=\dfrac{7\times6}{2}[/tex]
[tex]=21[/tex]
Hence, 21 line segments are needed to connect each dot to each other dot.
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