Question 1178570
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Let think that the grid is 3 points vertically and 5 points horizontally.


Then there are THESE families of straight line segments satisfying imposed conditions


    3 x 3 = 9 horizontal segments of the length 2

            3 horizontal segments of the length 4


            5 vertical segments of the length   2


            1 sloped segment    of the slope   2/4 = 1/2

            3 sloped segments   of the slope     1

            3 sloped segments   of the slope    -1

            1 sloped segment    of the slope  -2/4 = -1/2


Counting this way, there are  9 + 3 + 5 + 1 + 3 + 3 + 1 = 25 segments satisfying the posed condition.
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Solved.