Grid6

A = (4.082188592760043, 3.191957058243276)
B = (4.466666120884486, 3.373096136033251)
d_{AB} = Distance(A, B)
θ: atan(Slope[Line[A, B]])
m = 4 (slider from 0 to 10, step 1)
n = 3 (slider from 0 to 10, step 1)
a = Segment(A, B)
GridAllParallelABsegments = Sequence(Segment[(x(A) - n * d_{AB} * cos(θ) - i * d_{AB} * sin(θ), y(A) - n * d_{AB} * sin(θ) + i * d_{AB} * cos(θ)), (x(A) + n * d_{AB} * cos(θ) - i * d_{AB} * sin(θ), y(A) + n * d_{AB} * sin(θ) + i * d_{AB} * cos(θ))], i, -m, m)