Check Collinearity of Three Points and Print Line Equation in Python

Program Overview

This Python program reads the coordinates of three points: A, B, and C.
It checks whether the three points lie on the same straight line.
If they are collinear, it prints the line equation in the form ax + by + c = 0.
Otherwise, it prints No.

Python Code:

def slope(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    if x2 - x1 == 0:
        return None  # Vertical line
    return (y2 - y1) / (x2 - x1)

def line_equation(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    a = y2 - y1
    b = x1 - x2
    c = x2 * y1 - x1 * y2
    return a, b, c

# Input
print("Enter coordinates of three points:")
x1, y1 = map(float, input("Point A (x y): ").split())
x2, y2 = map(float, input("Point B (x y): ").split())
x3, y3 = map(float, input("Point C (x y): ").split())

# Check collinearity
m1 = slope((x1, y1), (x2, y2))
m2 = slope((x2, y2), (x3, y3))

if m1 == m2:
    a, b, c = line_equation((x1, y1), (x2, y2))
    print(f"Line equation: {a}x + {b}y + {c} = 0")
else:
    print("No")

Sample Output:

Point A (x y): 1 2  
Point B (x y): 2 4  
Point C (x y): 3 6  

Line equation: 2x + -1y + 0 = 0

Step-by-Step Explanation:

- The program calculates the slope between points A and B, and between B and C
- If the slopes are equal, the points are collinear
- Then it computes the line equation using points A and B
- If the slopes differ, the output is No