[Python] Why GCD is needed in this algorithm finding all groups of three points are collinear...

I was trying to solve this coding challenge: "Given an array of pairs, each pair (x, y), which are both integer, denotes coordinate of a point in Cartesian coordinate plane, find many groups of three points are collinear."

It turns out this below is the correct algorithm:

def gcd(x, y):
if y == 0:
return x
else:
return gcd(y, x % y)

def how_many_3point_in_line( points ):
ans = 0
n = len( points )
for i in range( n - 2 ):
slopes = defaultdict( int )
for j in range( i + 1, n ):
dy, dx = points[1] - points[j][1], points[0] - points[j][0]
gcd_num = gcd( dx, dy )
slopes[( dy // gcd_num, dx // gcd_num )] += 1
for _, occ in slopes.items():
ans += math.comb( occ, 2 )
return ans


Apparently the gcd is used to represent slope, what issue does it address?

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