Python Program for Section Formula (Point that Divides a Line in Given Ratio)

In the previous article, we have discussed Python Program to Find the Mid-Point of a Line
Given two points of a line and P, Q, the task is to find the point that divides the line in the given ratio P: Q in Python.

The section formula gives us the coordinates of the point that divides a given line segment into two parts with lengths that are in the ratio m: n.

Section Formula:
(mx2+nx1)/(m+n), (my2+ny1)/(m+n)

Examples:

Example1:

Input:

Given First Point = ( 2, 4 )
Given Second Point = ( 1, 3 )
Given ratio value p= 1
Given ratio value q= 2

Output:

The point that divides the line in the given ratio ( 1 : 2 ) is :
( 1.6666666666666667 , 3.6666666666666665 )

Example2:

Input:

Given First Point = ( 5, 7)
Given Second Point = ( 2, 8 )
Given ratio value p= 2
Given ratio value q= 5

Output:

The point that divides the line in the given ratio ( 2 : 5 ) is :
( 4.142857142857143 , 7.285714285714286 )

Program for Section Formula (Point that Divides a Line in Given Ratio) in Python:

Below are the ways to find the point that divides the line in the given ratio P: Q in Python:

Using Mathematical Formula (Static Input)
Using Mathematical Formula (User Input)

Method #1: Using Mathematical Formula (Static Input)

Approach:

Give the first point as static input and store it in two variables.
Give the second point as static input and store it in another two variables.
Give the ratio values p, q as static input and store them in two separate variables.
Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments to the Find_Section() function.
Create a function to say Find_Midpoint() which takes the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point that divides the line in the given ratio p: q.
Inside the function calculate the x coordinate of the point using the mathematical formula (q * a1)+(p * a2))/(p + q) and convert it into float using the float() function.
Store it in a variable.
Calculate the y coordinate of the point using the mathematical formula (q * b1)+(p * b2))/(p + q) and convert it into float using the float() function.
Store it in another variable.
Print the point that divides the line in the given ratio p: q.
The Exit of the Program.

Below is the implementation:

# Create a function to say Find_Midpoint() which takes the given two points of a line
# and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point
# that divides the line in the given ratio p: q.


def Find_Section(a1, a2, b1, b2, p, q):
    # Inside the function calculate the x coordinate of the point using the mathematical
    # formula (q * a1)+(p * a2))/(p + q) and convert it into float
    # using the float() function.
    # Store it in a variable.
    x_coordinate = (float)((q * a1)+(p * a2))/(p + q)
    # Calculate the y coordinate of the point using the mathematical formula
    # (q * b1)+(p * b2))/(p + q) and convert it into float using the
    # float() function.
    # Store it in another variable.
    y_coordinate = (float)((q * b1)+(p * b2))/(p + q)

    # Print the point that divides the line in the given ratio p: q.
    print("(", x_coordinate, ",", y_coordinate, ")")


# Give the first point as static input and store it in two variables.
a1 = 2
b1 = 4
# Give the second point as static input and store it in another two variables.
a2 = 1
b2 = 3
p = 1
q = 2
print("The point that divides the line in the given ratio (", p, ":", q, ") is :")
# Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as
# the arguments to the Find_Section() function.
Find_Section(a1, a2, b1, b2, p, q)

Output:

The point that divides the line in the given ratio ( 1 : 2 ) is :
( 1.6666666666666667 , 3.6666666666666665 )

Method #2: Using Mathematical Formula (User Input)

Approach:

Give the first point as user input using map(),int(),split() functions and store it in two variables.
Give the second point as user input using map(),int(),split() functions and store it in two variables.
Give the ratio values p, q as static input and store them in two separate variables.
Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments to the Find_Section() function.
Create a function to say Find_Midpoint() which takes the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point that divides the line in the given ratio p: q.
Inside the function calculate the x coordinate of the point using the mathematical formula (q * a1)+(p * a2))/(p + q) and convert it into float using the float() function.
Store it in a variable.
Calculate the y coordinate of the point using the mathematical formula (q * b1)+(p * b2))/(p + q) and convert it into float using the float() function.
Store it in another variable.
Print the point that divides the line in the given ratio p: q.
The Exit of the Program.

Below is the implementation:

# Create a function to say Find_Midpoint() which takes the given two points of a line
# and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point
# that divides the line in the given ratio p: q.


def Find_Section(a1, a2, b1, b2, p, q):
    # Inside the function calculate the x coordinate of the point using the mathematical
    # formula (q * a1)+(p * a2))/(p + q) and convert it into float
    # using the float() function.
    # Store it in a variable.
    x_coordinate = (float)((q * a1)+(p * a2))/(p + q)
    # Calculate the y coordinate of the point using the mathematical formula
    # (q * b1)+(p * b2))/(p + q) and convert it into float using the
    # float() function.
    # Store it in another variable.
    y_coordinate = (float)((q * b1)+(p * b2))/(p + q)

    # Print the point that divides the line in the given ratio p: q.
    print("(", x_coordinate, ",", y_coordinate, ")")


# Give the first point as user input using map(),int(),split() functions
# and store it in two variables.
a1, b1 = map(int, input(
    'Enter some random first point values separated by spaces = ').split())
# Give the second point as user input using map(),int(),split() functions
# and store it in two variables.
a2, b2 = map(int, input(
    'Enter some random second point values separated by spaces = ').split())
p = 2
q = 5
print("The point that divides the line in the given ratio (", p, ":", q, ") is :")
# Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as
# the arguments to the Find_Section() function.
Find_Section(a1, a2, b1, b2, p, q)

Output:

Enter some random first point values separated by spaces = 5 7
Enter some random second point values separated by spaces = 2 8
The point that divides the line in the given ratio ( 2 : 5 ) is :
( 4.142857142857143 , 7.285714285714286 )

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