Show That The Points 11 52 And 9 5 Are Collinear-class-10-maths-CBSE

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsShow that the points (1,-1), (5,2) and (9, 5) are collinear.AnswerVerified602.7k+ viewsHint: Here we will check whether the given points are collinear or not by using the condition of collinearity i.e., sum of length any two segments equal to the length of the remaining line segment.Complete step-by-step answer:Three or more points A, B, C ….. are said to be collinear if they lie on a single straight line.The given points are\[A = (1, - 1),B = (5,2){\text{ and }}C = (9,5)\]Distance between any two points with coordinates $(x_1, y_1)$ and $(x_2, y_2)$ is given by$ \Rightarrow d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_2})}^2}} $Now, calculating the distance between A & B$AB = \sqrt {{{(5 - 1)}^2} + {{(2 + 1)}^2}} = \sqrt {16 + 9} = \sqrt {25} = 5$Now, calculating the distance between B & C$BC = \sqrt {{{(5 - 9)}^2} + {{(2 - 5)}^2}} = \sqrt {16 + 9} = \sqrt {25} = 5$Now, calculating the distance between A & C$AC = \sqrt {{{(1 - 9)}^2} + {{( - 1 - 5)}^2}} = \sqrt {64 + 36} = \sqrt {100} = 10$Clearly, $AC = AB + BC$Hence, A, B, C are collinear points.Note: If the sum of the lengths of any two line segments among AB, BC, and AC is equal to the length of the remaining line segment then the points are collinear otherwise not. Another way to find collinearity is to substitute the coordinates of all the three points in the area of triangle formula. If the area value is 0 then the points are collinear else they are non collinear.Recently Updated PagesMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Biology: Engaging Questions & Answers for SuccessMaster Class 12 Physics: Engaging Questions & Answers for SuccessMaster Class 8 Maths: Engaging Questions & Answers for SuccessClass 8 Question and Answer - Your Ultimate Solutions GuideMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Biology: Engaging Questions & Answers for SuccessMaster Class 12 Physics: Engaging Questions & Answers for SuccessMaster Class 8 Maths: Engaging Questions & Answers for SuccessClass 8 Question and Answer - Your Ultimate Solutions Guide

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