I'm having a problem with determining the intersection of two lines in this python code

It's hard to dig through your code. Especially c_line1 = -((a_line1*point1_line1[0]) + (b_line1*point1_line1[1])) seems to be odd, because it calculates the Dot product of vector and a point.
Therefore I don't know exactly what's wrong with your code, but I know how to intersect lines. See Problem with calculating line intersections and Collision and Intersection - Line and line.

Write functions that can add, subtract, scale vectors and rotate vectors by 90°. Write a function which calculates the Dot product:

def add(a, b): return a[0]+b[0], a[1]+b[1] def sub(a, b): return a[0]-b[0], a[1]-b[1] def rot90(v): return -v[1], v[0] def mul(v, s): return v[0]*s, v[1]*s def dot(a, b): return a[0]*b[0] + a[1]*b[1] 

Calculate the vector from the beginning of the lines to the end of the lines and the normal vectors to the lines. The normal vector is obtained by rotating the line vector by 90°:

#line 1 point1_line1, point2_line1 = lines[0] line1_vector = sub(point2_line1, point1_line1) line1_norml = rot90(line1_vector) #line2 point1_line2, point2_line2 = lines[1] line2_vector = sub(point2_line2, point1_line2) line2_norml = rot90(line2_vector) 

Calculate the intersection of the line segments. Make sure the lines are not parallel and that the intersection point is on the line segments:

# vector from start point of line 2 to start point of line 1 l2p1_l1p1 = sub(point1_line1, point1_line2) # intersection d = dot(line2_vector, line1_norml) if d != 0: # prallel lines t = dot(l2p1_l1p1, line1_norml) / d u = dot(l2p1_l1p1, line2_norml) / d if 0 <= t <= 1 and 0 <= u <= 1: # intersection on line segments xi, yi = add(point1_line2, mul(line2_vector, t)) 

Minimal example:

from pygame import * init() win = display.set_mode((500,500)) lines = [] cords = [] preview = False xi, yi = -100, -100 def drawlines(flines): for fcords in flines: draw.line(win,(0,0,0),fcords[0],fcords[1],4) def add(a, b): return a[0]+b[0], a[1]+b[1] def sub(a, b): return a[0]-b[0], a[1]-b[1] def rot90(v): return -v[1], v[0] def mul(v, s): return v[0]*s, v[1]*s def dot(a, b): return a[0]*b[0] + a[1]*b[1] run = True while run: for ev in event.get(): if ev.type == QUIT: run = False elif ev.type == MOUSEBUTTONDOWN: if ev.button == 1: preview = True a = ev.pos cords.append(a) elif ev.type == MOUSEBUTTONUP: if ev.button == 1: cords.append(ev.pos) lines.append((cords)) cords = [] preview = False intersections = [] for i, line1 in enumerate(lines): for line2 in lines[i+1:]: #line 1 point1_line1, point2_line1 = line1 line1_vector = sub(point2_line1, point1_line1) line1_norml = rot90(line1_vector) #line2 point1_line2, point2_line2 = line2 line2_vector = sub(point2_line2, point1_line2) line2_norml = rot90(line2_vector) # vector from start point of line 2 to start point of line 1 l2p1_l1p1 = sub(point1_line1, point1_line2) # intersection d = dot(line2_vector, line1_norml) if d != 0: # prallel lines t = dot(l2p1_l1p1, line1_norml) / d u = dot(l2p1_l1p1, line2_norml) / d if 0 <= t <= 1 and 0 <= u <= 1: # intersection on line segments xi, yi = add(point1_line2, mul(line2_vector, t)) intersections.append((xi, yi)) win.fill((255,255,255)) if len(cords) % 2 == 1: draw.line(win,(0,0,0), a, mouse.get_pos(), 4) drawlines(lines) for p in intersections: draw.circle(win, (0,200,0), (round(p[0]), round(p[1])), 10) display.flip() quit() exit()