Python: Test whether two lines PQ and RS are parallel

Last update on December 21 2024 07:19:27 (UTC/GMT +8 hours)

Parallel Lines Tester

Write a Python program to test whether two lines PQ and RS are parallel. The four points are P(x1, y1), Q(x2, y2), R(x3, y3), S(x4, y4).

Input:
x1,y1,x2,y2,x3,y3,xp,yp separated by a single space

Sample Solution:

Python Code:

# Print statement to prompt the user to input coordinates of two line segments (PQ and RS)
print("Input x1, y1, x2, y2, x3, y3, x4, y4:")

# Take user input for coordinates of the two line segments and convert them to float
x1, y1, x2, y2, x3, y3, x4, y4 = map(float, input().split())

# Check if PQ and RS are parallel using the cross product of their direction vectors
# The condition uses a small tolerance (1e-10) to handle floating-point precision issues
print('PQ and RS are parallel.' if abs((x2 - x1)*(y4 - y3) - (x4 - x3)*(y2 - y1)) < 1e-10 else 'PQ and RS are not parallel')

Sample Output:

Input x1,y1,x2,y2,x3,y3,xp,yp:
 2 5 6 4 8 3 9 7
PQ and RS are not parallel

Explanation:

Here is a breakdown of the above Python code:

• The code begins by printing a message to prompt the user to input the coordinates of two line segments (PQ and RS).
• User input is obtained, where coordinates are separated by spaces and converted to floating-point numbers.
• The code then checks if the two line segments PQ and RS are parallel using the cross product of their direction vectors.
• The condition (x2 - x1)*(y4 - y3) - (x4 - x3)*(y2 - y1) compares the cross product with a small tolerance (1e-10).
• Depending on the result of the condition, the code prints whether PQ and RS are parallel or not.

Flowchart:

Python Code Editor:

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