write a python function to check if the two lines are perpendicular

Perpendicular Lines

Perpendicular lines stand in stark contrast to parallel lines, their paths intersecting at a right angle, forming a 90-degree angle. To determine whether two lines are perpendicular, we must delve into the world of slopes. The slope of a line, often denoted by 'm', represents the gradient of the line, indicating its steepness and direction.

For two lines to be perpendicular, their slopes must be negative reciprocals of each other. In simpler terms, if the slope of one line is 'm', the slope of the perpendicular line must be '-1/m'. This reciprocal relationship arises from the fact that when lines intersect at a right angle, their slopes multiply to give -1.

 

Unleashing Python's Prowess: A Function to Detect Perpendicularity

Now, let's harness the power of Python to translate this geometric concept into an executable program. We'll create a function that takes the slopes of two lines as input and determines whether they are perpendicular.

Python

def check_perpendicularity(m1, m2):
    if m1 * m2 == -1:
        return True
    else:
        return False

This concise code encapsulates the perpendicularity test within the check_perpendicularity function. It compares the slopes 'm1' and 'm2' and checks if their product equals -1. If the condition is met, the function returns 'True', indicating perpendicularity. Otherwise, it returns 'False'.

 

 

Testing the Function: Unveiling Perpendicularity

To validate our function, let's put it to the test. Consider two lines:

• Line 1: with slope m1 = 2
• Line 2: with slope m2 = -1/2

Python

perpendicular = check_perpendicularity(2, -1/2)
if perpendicular:
    print("The lines are perpendicular")
else:
    print("The lines are not perpendicular")

Running this code should yield the output:

The lines are perpendicular

This confirms that our function correctly identifies the perpendicular relationship between the two lines.

 

 

Conclusion: A Conquest in the Geometric Realm

Our journey through the geometric realm has led us to a successful conquest of determining perpendicularity between two lines. We have employed the concept of slopes, their reciprocal relationship with perpendicularity, and harnessed Python's power to uncover this geometrical connection. As we continue our programming adventures, may these newfound skills serve as guiding lights in our quest for geometric mastery.