{"id":6925,"date":"2021-10-22T01:38:53","date_gmt":"2021-10-21T20:08:53","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6925"},"modified":"2021-10-25T09:52:45","modified_gmt":"2021-10-25T04:22:45","slug":"if-the-line-2x-y-k-passes-through-the-point-which-divides-the-line-segment-joining-the-points-11-and-24-in-the-ratio-32-then-k-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-line-2x-y-k-passes-through-the-point-which-divides-the-line-segment-joining-the-points-11-and-24-in-the-ratio-32-then-k-is-equal-to\/","title":{"rendered":"If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to"},"content":{"rendered":"

Solution :<\/h2>\n

Given line L : 2x + y = k passes through point (Say P) which divides the line segment (let AB) in ration 3:2, where A(1, 1) and B(2, 4).<\/p>\n

Using section formula, the coordinates of the point P which divides AB internally in the ratio 3:2 are<\/p>\n

P(\\(3\\times 2 + 2\\times 1\\over 3 + 2\\), \\(3\\times 4 + 2\\times 1\\over 3 + 2\\)) = P(\\(8\\over 5\\), \\(14\\over 5\\))<\/p>\n

Also, since the line L passes through P, hence substituting the coordinates of P(\\(8\\over 5\\), \\(14\\over 5\\)) in the equation of L : 2x + y = k, we get<\/p>\n

2(\\(8\\over 5\\)) + \\(14\\over 5\\) = k<\/p>\n

\\(\\implies\\) k = 6<\/p>\n

\n

Similar Questions<\/h3>\n

Find the distance between the line 12x \u2013 5y + 9 = 0 and the point (2,1)<\/a><\/p>\n

If p is the length of the perpendicular from the origin to the line \\(x\\over a\\) + \\(y\\over b\\) = 1, then prove that \\(1\\over p^2\\) = \\(1\\over a^2\\) + \\(1\\over b^2\\)<\/a><\/p>\n

If \\(\\lambda x^2 \u2013 10xy + 12y^2 + 5x \u2013 16y \u2013 3\\) = 0 represents a pair of straight lines, then \\(\\lambda\\) is equal to<\/a><\/p>\n

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes, then<\/a><\/p>\n

If PS is the median of the triangle, with vertices of P(2,2), Q(6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given line L : 2x + y = k passes through point (Say P) which divides the line segment (let AB) in ration 3:2, where A(1, 1) and B(2, 4). Using section formula, the coordinates of the point P which divides AB internally in the ratio 3:2 are P(\\(3\\times 2 + 2\\times 1\\over …<\/p>\n

If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to<\/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":[43,48],"tags":[],"yoast_head":"\nIf the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to<\/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:\/\/mathemerize.com\/if-the-line-2x-y-k-passes-through-the-point-which-divides-the-line-segment-joining-the-points-11-and-24-in-the-ratio-32-then-k-is-equal-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to\" \/>\n<meta property=\"og:description\" content=\"Solution : Given line L : 2x + y = k passes through point (Say P) which divides the line segment (let AB) in ration 3:2, where A(1, 1) and B(2, 4). 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