{"id":3892,"date":"2021-08-09T20:48:49","date_gmt":"2021-08-09T20:48:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3892"},"modified":"2021-11-30T16:40:07","modified_gmt":"2021-11-30T11:10:07","slug":"formula-for-angle-between-two-lines","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-angle-between-two-lines\/","title":{"rendered":"Formula for Angle between Two Lines"},"content":{"rendered":"

Here, you will learn formula for angle between two lines, equation of straight line making an angle with a given line and reflection and image of a point in a line and also length of perpendicular from a point on a line.<\/p>\n

Let’s begin –<\/p>\n

Angle between Two Lines<\/h2>\n

(a)\u00a0 If \\(\\theta\\) be the angle between two lines : y = \\(m_1x + c_1\\) and y = \\(m_2x + c_2\\), then<\/p>\n

\n

tan\\(\\theta\\) = \\(\\pm\\) (\\(m_1-m_2\\over {1+m_1m_2}\\))<\/p>\n<\/blockquote>\n

(b)\u00a0 If the equation of lines are \\(a_1x + b_1y + c_1\\) = 0 and \\(a_2x + b_2y + c_2\\) = 0, then these lines are –\u00a0<\/p>\n

\n

(i)\u00a0 Parallel\u00a0 \\(\\iff\\)\u00a0 \u00a0\\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) \\(\\ne\\) \\(c_1\\over c_2\\)<\/p>\n

(ii)\u00a0 Perpendicular\u00a0 \\(\\iff\\)\u00a0 \\(a_1a_2\\) + \\(b_1b_2\\) = 0<\/p>\n

(iii)\u00a0 Coincident\u00a0 \\(\\iff\\)\u00a0 \\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) = \\(c_1\\over c_2\\)<\/p>\n<\/blockquote>\n

Equation of Straight line making an angle with a Line :<\/strong><\/p>\n

Equation of line passing through a point (\\(x_1,y_1\\)) and making an angle \\(\\alpha\\), with the line y = mx + c is written as<\/p>\n

\n

y – \\(y_1\\) = \\(m \\pm tan\\alpha\\over {1 \\mp mtan\\alpha}\\)(x – \\(x_1\\))<\/p>\n<\/blockquote>\n

Reflection and image of a point in a line :<\/h2>\n

Let P(x,y) be any point, then its image with respect to<\/p>\n

(a)\u00a0 x-axis is Q(x,-y)<\/p>\n

(b)\u00a0 y-axis is R(-x, y)<\/p>\n

(c)\u00a0 origin is S(-x,-y)<\/p>\n

(d)\u00a0 line y = x is T(y,x)<\/p>\n

(e)\u00a0 Reflection of a point about any arbitrary line : The image (h,k) of a point P(\\(x_1,y_1\\)) about the line ax+by+c = 0 is given by following formula.<\/p>\n

\n

\\(h-x_1\\over a\\) = \\(k-y_1\\over b\\) = -2(\\(ax_1+by_1+c\\over {a^2+b^2}\\))<\/p>\n<\/blockquote>\n

and the foot of perpendicular (p,q) from a point (\\(x_1,y_1\\)) on the line ax+by+c = 0 is given by following formula.<\/p>\n

\n

\\(p-x_1\\over a\\) = \\(q-y_1\\over b\\) = -(\\(ax_1+by_1+c\\over {a^2+b^2}\\))<\/p>\n<\/blockquote>\n

Length of perpendicular from a point on a line :<\/h2>\n

Length of perpendicular from a point (\\(x_1,y_1\\)) on the line ax + by + c = 0 is<\/p>\n

\n

|\\(ax_1 + by_1 + c\\over {\\sqrt{a^2+b^2}}\\)|<\/p>\n<\/blockquote>\n

In particular, the length of perpendicular from the origin on the line ax + by + c = 0 is<\/p>\n

\n

P = \\(|c|\\over {\\sqrt{a^2+b^2}}\\).<\/p>\n<\/blockquote>\n

Hope you learnt formula for angle between two lines and all other concepts. Practice more questions to learn more and get ahead in competition. Good Luck!<\/p>\n\n\n

\n
Next – How to Find slope of Line \u2013 Slope of Parallel Lines<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of Straight Lines in all Forms<\/a><\/div>\n<\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn formula for angle between two lines, equation of straight line making an angle with a given line and reflection and image of a point in a line and also length of perpendicular from a point on a line. Let’s begin – Angle between Two Lines (a)\u00a0 If \\(\\theta\\) be the angle …<\/p>\n

Formula for Angle between Two 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":[654,655],"yoast_head":"\nFormula for Angle between Two Lines - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn formula for angle between two lines and equation of straight line making an angle with a given line.\" \/>\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\/formula-for-angle-between-two-lines\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Angle between Two Lines - 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