{"id":22725,"date":"2021-09-27T15:43:09","date_gmt":"2021-09-27T10:13:09","guid":{"rendered":"https:\/\/python-programs.com\/?p=22725"},"modified":"2021-11-22T18:35:38","modified_gmt":"2021-11-22T13:05:38","slug":"python-program-for-section-formula-point-that-divides-a-line-in-given-ratio","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-section-formula-point-that-divides-a-line-in-given-ratio\/","title":{"rendered":"Python Program for Section Formula (Point that Divides a Line in Given Ratio)"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-find-the-mid-point-of-a-line\/\">Python Program to Find the Mid-Point of a Line<\/a><br \/>\nGiven 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.<\/p>\n<p>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.<\/p>\n<blockquote><p><strong>Section Formula:<\/strong><\/p>\n<p>(mx2+nx1)\/(m+n), (my2+ny1)\/(m+n)<\/p><\/blockquote>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given First Point = ( 2, 4 )\r\nGiven Second Point = ( 1, 3 )\r\nGiven ratio value p= 1\r\nGiven ratio value q= 2<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The point that divides the line in the given ratio ( 1 : 2 ) is :\r\n( 1.6666666666666667 , 3.6666666666666665 )<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given First Point = ( 5, 7)\r\nGiven Second Point = ( 2, 8 )\r\nGiven ratio value p= 2\r\nGiven ratio value q= 5<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The point that divides the line in the given ratio ( 2 : 5 ) is :\r\n( 4.142857142857143 , 7.285714285714286 )<\/pre>\n<h2>Program for Section Formula (Point that Divides a Line in Given Ratio) in Python:<\/h2>\n<p>Below are the ways to find the point that divides the line in the given ratio P: Q in Python:<\/p>\n<ul>\n<li><a href=\"#Using_Mathematical_Formula_(Static_Input)\">Using Mathematical Formula (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Mathematical_Formula_(User_Input)\">Using Mathematical Formula (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Mathematical_Formula_(Static_Input)\">Method #1: Using Mathematical Formula (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the first point as static input and store it in two variables.<\/li>\n<li>Give the second point as static input and store it in another two variables.<\/li>\n<li>Give the ratio values p, q as static input and store them in two separate variables.<\/li>\n<li>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<strong> Find_Section()<\/strong> function.<\/li>\n<li>Create a function to say <strong>Find_Midpoint()<\/strong> 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.<\/li>\n<li>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.<\/li>\n<li>Store it in a variable.<\/li>\n<li>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.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Print the point that\u00a0divides the line in the given ratio p: q.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a function to say Find_Midpoint() which takes the given two points of a line\r\n# and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point\r\n# that divides the line in the given ratio p: q.\r\n\r\n\r\ndef Find_Section(a1, a2, b1, b2, p, q):\r\n    # Inside the function calculate the x coordinate of the point using the mathematical\r\n    # formula (q * a1)+(p * a2))\/(p + q) and convert it into float\r\n    # using the float() function.\r\n    # Store it in a variable.\r\n    x_coordinate = (float)((q * a1)+(p * a2))\/(p + q)\r\n    # Calculate the y coordinate of the point using the mathematical formula\r\n    # (q * b1)+(p * b2))\/(p + q) and convert it into float using the\r\n    # float() function.\r\n    # Store it in another variable.\r\n    y_coordinate = (float)((q * b1)+(p * b2))\/(p + q)\r\n\r\n    # Print the point that\u00a0divides the line in the given ratio p: q.\r\n    print(\"(\", x_coordinate, \",\", y_coordinate, \")\")\r\n\r\n\r\n# Give the first point as static input and store it in two variables.\r\na1 = 2\r\nb1 = 4\r\n# Give the second point as static input and store it in another two variables.\r\na2 = 1\r\nb2 = 3\r\np = 1\r\nq = 2\r\nprint(\"The point that divides the line in the given ratio (\", p, \":\", q, \") is :\")\r\n# Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as\r\n# the arguments to the Find_Section() function.\r\nFind_Section(a1, a2, b1, b2, p, q)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The point that divides the line in the given ratio ( 1 : 2 ) is :\r\n( 1.6666666666666667 , 3.6666666666666665 )<\/pre>\n<h3 id=\"Using_Mathematical_Formula_(User_Input)\">Method #2: Using Mathematical Formula (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the first point as user input using map(),int(),split() functions and store it in two variables.<\/li>\n<li>Give the second point as user input using map(),int(),split() functions and store it in two variables.<\/li>\n<li>Give the ratio values p, q as static input and store them in two separate variables.<\/li>\n<li>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<strong> Find_Section()<\/strong> function.<\/li>\n<li>Create a function to say <strong>Find_Midpoint()<\/strong> 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.<\/li>\n<li>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.<\/li>\n<li>Store it in a variable.<\/li>\n<li>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.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Print the point that\u00a0divides the line in the given ratio p: q.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a function to say Find_Midpoint() which takes the given two points of a line\r\n# and the ratio values i.e, a1, a2, b1, b2, p, q as the arguments and prints the point\r\n# that divides the line in the given ratio p: q.\r\n\r\n\r\ndef Find_Section(a1, a2, b1, b2, p, q):\r\n    # Inside the function calculate the x coordinate of the point using the mathematical\r\n    # formula (q * a1)+(p * a2))\/(p + q) and convert it into float\r\n    # using the float() function.\r\n    # Store it in a variable.\r\n    x_coordinate = (float)((q * a1)+(p * a2))\/(p + q)\r\n    # Calculate the y coordinate of the point using the mathematical formula\r\n    # (q * b1)+(p * b2))\/(p + q) and convert it into float using the\r\n    # float() function.\r\n    # Store it in another variable.\r\n    y_coordinate = (float)((q * b1)+(p * b2))\/(p + q)\r\n\r\n    # Print the point that\u00a0divides the line in the given ratio p: q.\r\n    print(\"(\", x_coordinate, \",\", y_coordinate, \")\")\r\n\r\n\r\n# Give the first point as user input using map(),int(),split() functions\r\n# and store it in two variables.\r\na1, b1 = map(int, input(\r\n    'Enter some random first point values separated by spaces = ').split())\r\n# Give the second point as user input using map(),int(),split() functions\r\n# and store it in two variables.\r\na2, b2 = map(int, input(\r\n    'Enter some random second point values separated by spaces = ').split())\r\np = 2\r\nq = 5\r\nprint(\"The point that divides the line in the given ratio (\", p, \":\", q, \") is :\")\r\n# Pass the given two points of a line and the ratio values i.e, a1, a2, b1, b2, p, q as\r\n# the arguments to the Find_Section() function.\r\nFind_Section(a1, a2, b1, b2, p, q)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random first point values separated by spaces = 5 7\r\nEnter some random second point values separated by spaces = 2 8\r\nThe point that divides the line in the given ratio ( 2 : 5 ) is :\r\n( 4.142857142857143 , 7.285714285714286 )<\/pre>\n<p>Access the big list of <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Programming Code Examples<\/a> with actual logical code asked in Programming and Coding Interviews for Python and stand out from the crowd.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-check-if-three-points-are-collinear\/\">Python Program to Check if Three Points are Collinear<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-nth-pentagonal-number\/\">Python Program to Find N\u2019th Pentagonal Number<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-line-passing-through-2-points\/\">Python Program to Find Line Passing Through 2 Points<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-mid-point-of-a-line\/\">Python Program to Find the Mid-Point of a Line<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>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 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-for-section-formula-point-that-divides-a-line-in-given-ratio\/\"> <span class=\"screen-reader-text\">Python Program for Section Formula (Point that Divides a Line in Given Ratio)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":22833,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program for Section Formula (Point that Divides a Line in Given Ratio) - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-for-section-formula-point-that-divides-a-line-in-given-ratio\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program for Section Formula (Point that Divides a Line in Given Ratio) - Python Programs\" \/>\n<meta property=\"og:description\" content=\"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. 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