{"id":4002,"date":"2021-08-13T17:03:14","date_gmt":"2021-08-13T17:03:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4002"},"modified":"2021-11-30T16:33:54","modified_gmt":"2021-11-30T11:03:54","slug":"what-is-the-section-formula","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-section-formula\/","title":{"rendered":"What is the Section Formula | Distance Formula"},"content":{"rendered":"
Here, you will learn what is the section formula and distance formula and and applications of distance formula.<\/p>\n
Let’s begin –<\/p>\n
The co-ordinates of a point dividing a line joining the points P(\\(x_1,y_1\\)) and Q(\\(x_2,y_2\\)) in the ratio m : n is given by :<\/p>\n
(a)\u00a0 for internal division :\u00a0<\/strong>R(x,y) divides line segment PQ, internally.<\/p>\n (x,y) = (\\(mx_2 + nx_1\\over {m+n}\\),\\(my_2 + ny_1\\over {m+n}\\))<\/p>\n<\/blockquote>\n (b) for external division :\u00a0<\/strong>R(x,y) divides line segment PQ, externally.<\/p>\n (x,y) = (\\(mx_2 – nx_1\\over {m-n}\\),\\(my_2 – ny_1\\over {m-n}\\))<\/p>\n<\/blockquote>\n (c) Harmonic Conjugate :\u00a0<\/strong>If P divides AB internally in the ratio m : n & Q divides AB externally in the ratio m : n then P & Q are said to be harmonic conjugate of each other w.r.t. AB.<\/p>\n Mathematically, \\(2\\over AB\\) = \\(1\\over AP\\) + \\(1\\over AQ\\) i.e. AP, AB & AQ are in H.P.<\/p>\n<\/blockquote>\n If A(\\(x_1,y_1\\)) and B(\\(x_2,y_2\\)) are two points, then<\/p>\n AB = \\(\\sqrt{{(x_2-x_1)}^2 + {(y_2-y_1)}^2}\\)<\/p>\n<\/blockquote>\n Note :<\/strong><\/p>\n (i) \u00a0Three given points A,B and C are collinear, when sum of any two distances out of AB, BC, CA is equal to the remaining third otherwise the points will be the vertices of a triangle.<\/p>\n (ii)\u00a0 Let A,B,C & D be the four points in a plane. Then the quadrilateral will be :<\/p>\n (a)\u00a0 Square if AB = BC = CD = DA & AC = BD\u00a0 \u00a0 AC \\(\\perp\\) BD<\/p>\n (b)\u00a0 Rhombus if AB = BC = CD = DA and AC \\(\\ne\\) BD\u00a0 \u00a0 AC \\(\\perp\\) BD<\/p>\n (c)\u00a0 Parallelogram if AB = BC = CD = DA ; AC \\(\\ne\\) BD\u00a0 \u00a0AC \\(\\not\\perp\\) BD<\/p>\n (d)\u00a0 Rectangle if AB = BC = CD = DA ; AC = BD\u00a0 \u00a0 AC \\(\\not\\perp\\) BD<\/p>\n Hope learnt what is the section formula and distance formula and and applications of distance formula. Tp learn more practice more questions and get ahead in competition. Good Luck!<\/p>\n\n\n\n
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Distance Formula Between Two Points and its Applications<\/h2>\n
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