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:

### 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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