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 answer:

q =  1

Step-by-step explanation:

p1:x+2 y7=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:x2y+1=0  x+2y7=0 x2y+1=0  x+2 y7=0 x2 y+1=0  x+2y=7 x2y=1  x=3 y=2  [x;y]AB 1<x=3<5 q=1

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