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 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  Pivot:Row1Row2 3b+c=5 b+c=1  Row231 Row1Row2 3b+c=5 0.67c=0.67  c=0.666666670.66666667=1 b=35c=351=2  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  Row2Row1Row2 x+2y=7 4y=8  y=48=2 x=72y=72 2=3  x=3 y=2  [x;y]  AB  1< x=3 < 5 q=1

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