Line intersect segment

Decide whether the line p : x + 2 y - 7 = 0 intersects the line segment given by points A[1, 1] and B[5, 3]

Correct result:

q =  1

Solution:

p1:x+2 y−7=0 p2:ax+by+c=0 a=1   a⋅ 1+b⋅ 1+c=0 a⋅ 5+b⋅ 3+c=0 1⋅ 1+b⋅ 1+c=0 1⋅ 5+b⋅ 3+c=0  b+c=−1 3b+c=−5  b=−2 c=1  p2:x−2y+1=0   x+2y−7=0 x−2y+1=0  x+2⋅ y−7=0 x−2⋅ y+1=0  x+2y=7 x−2y=−1  x=3 y=2  [x;y]∈AB 1<x=3<5 q=1

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