{"id":2909,"date":"2021-07-16T13:05:23","date_gmt":"2021-07-16T13:05:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=2909"},"modified":"2021-10-07T15:38:53","modified_gmt":"2021-10-07T10:08:53","slug":"how-to-find-the-distance-between-two-parallel-lines","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/how-to-find-the-distance-between-two-parallel-lines\/","title":{"rendered":"How to Find the Distance Between Two Parallel Lines"},"content":{"rendered":"

Distance Between Two Parallel Lines<\/h2>\n

If two lines are parallel, then they have the same distance between them throughout,<\/p>\n

Therefore the distance between two parallel lines\u00a0 \\(ax + by + c_1\\) and \\(ax + by + c_2\\) is given by :<\/p>\n

\n

D = \\(|c_1 – c_2|\\over \\sqrt{a^2 + b^2}\\)<\/p>\n<\/blockquote>\n

Note<\/strong> \u2013 Both equation must be in the given form \u00a0\\(ax + by + c_1\\) and \\(ax + by + c_2\\), if it is not in the given form reduce them to the given form as shown in the example below.<\/p>\n\n\n

Example : <\/span>Find the the distance between two parallel lines 3x – 4y + 9 and 6x – 8y – 15 = 0.<\/p>\n

Solution : <\/span>Given lines are 3x – 4y + 9 and 6x – 8y – 15 = 0.

\n Divide line 6x – 8y – 15 = 0 by 2

\n we get, 3x – 4y – 15\/2 = 0.

\n Now both the equation are reduced to given form.

\n Hence, we can find the distance using above formula

\n D = \\(|c_1 – c_2|\\over \\sqrt{a^2 + b^2}\\)

\n Required distance D = \\(|9 – (-15\/2)|\\over \\sqrt{3^2 + (-4)^2}\\)

\n D = \\(9 + {15\\over 2}\\over 5\\) = \\(33\\over 10\\)<\/p>\n\n\n\n

Example : <\/span>Find the equation of lines parallel to 3x – 4y – 5 = 0 at a unit distance from it.<\/p>\n

Solution : <\/span>Equation of any line parallel to 3x – 4y – 5 = 0 is

\n 3x – 4y + \\(\\lambda\\) = 0 …..(i)

\n It is given that the distance between the line 3x – 4y – 5 = 0 and line (i) is 1 unit.

\n \\(\\therefore\\) \\(|\\lambda – (-5)|\\over \\sqrt{3^2 + (-4)^2}\\) = 1

\n \\(\\implies\\) \\(|\\lambda + 5|\\over 5\\) = 1

\n \\(|\\lambda + 5|\\) = 5 \\(\\implies\\) \\(\\lambda + 5\\) = \\(\\pm 5\\)

\n \\(\\implies\\) \\(\\lambda\\) = 0 , -10

\n Substituting the values of \\(\\lambda\\) in (i), we get

\n3x – 4y = 0 and 3x – 4y – 10 = 0

\nas the equations of required lines.<\/p>\n\n\n\n

\n
Next – What is the Formula for Triangle Area ?<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – How to Find slope of Line \u2013 Slope of Parallel Lines<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Distance Between Two Parallel Lines If two lines are parallel, then they have the same distance between them throughout, Therefore the distance between two parallel lines\u00a0 \\(ax + by + c_1\\) and \\(ax + by + c_2\\) is given by : D = \\(|c_1 – c_2|\\over \\sqrt{a^2 + b^2}\\) Note \u2013 Both equation must be …<\/p>\n

How to Find the Distance Between Two Parallel Lines<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[32],"tags":[],"yoast_head":"\nHow to Find the Distance Between Two Parallel Lines - Mathemerize<\/title>\n<meta name=\"description\" content=\"Learn how to find the distance between two parallel lines and formula of distance between parallel lines with examples here.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/how-to-find-the-distance-between-two-parallel-lines\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Find the Distance Between Two Parallel Lines - 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