# find the value of k if the points are collinear

the will not form triangle m = \frac{ y_2 - y_1}{x_2 - x_1} they will lie on the same line, That is, if three points A(x 1, y 1) B(x 2, y 2) and C(x 3, y 3) will be collinear, then the area of triangle ABC = 0. x2 = 5 , y2 = 1 7k + 5k = 10 + 9 7 asked Oct 2, 2018 in Mathematics by Samantha ( 38.8k points) coordinate geometry or We can say that x3 = 2 , y3 = 5 Using the above concept, we can find the missing coordinate in the given points. Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. Zigya App. 2k = 8 Putting values Find the value of ‘K’ if the points (K, 3), (6, -2) and (-3, 4) are collinear. Check - Coordinate Geometry - Class 10, Ex 7.3 , 2 (7, 2), (5, 1), (3, k) He has been teaching from the past 9 years. Terms of Service. Here {/eq} is given by the formula -, {eq}\displaystyle 1/2 [ x1(y2 y3) + x2(y3 y1) + x3(y1 y2) ] = 0 If the above points are collinear, We need to find the value of {eq}\displaystyle 6k = 10 8 Putting values x2 = k , y2 = 4 7(1 k) + 5(k +2) + 3( 3) = 0 2 k = ( 8)/( 2) The idea is to understand that if three points are collinear they lie on the same line. Coordinate Geometry. (7, 2), (5, 1), (3, k) Let the given points be A (7, 2) , B (5, 1) , C (3, k) If the above points are collinear, they will lie on the same line, i.e. Services, Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More, Working Scholars® Bringing Tuition-Free College to the Community. 1/2 [ 7(1 k) + 5(k ( 2)) + 3( 2 1) ] = 0 8 6k + 10 = 0 x1 = 8 , y1 = 1 or We can say that Given A (2, 3), B (4, k) and C (6, -3) are collinear To find: Find the value of K So, The given points are collinear, if are (∆ABC) = 0 = 2k+6 - 24 +18 - 6k = 0 Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. 1/2 [ x1(y2 y3) + x2(y3 y1) + x3(y1 y2) ] = 0 the will not form triangle Question 1 : Find the value of ‘a’ for which the given points are collinear. Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear. Learn all Concepts of Chapter 7 Class 10 (with VIDEOS). 1/2 [ 8( 4 ( 5)) + k( 5 1) + 2(1 ( 4)) ] = 0 Let the given points be A(8, 1) , B(k, 4) , C(2, 5) Create your account. Ex 7.3 , 2 In each of the following find the value of k , for which the points are collinear. Teachoo provides the best content available! (-2,5), (-5,-10) On signing up you are confirming that you have read and agree to We need to find the value of k k such that the points (−2,5),(−5,−10) (− 2, 5), (− 5, − 10) and (k,−13) (k, − 13) are collinear. In each of the following find the value of k , for which the points are collinear. 8(1) + k( 6) + 2(5) = 0 If the above points are collinear, they will lie on the same line, i.e. Here Given three points, arc collinear if. k = 4 -2) and C (-3, 4). All other trademarks and copyrights are the property of their respective owners. {/eq} such that the points {eq}\displaystyle k Find the value of k, if the points (-2,5), (-5,-10) and (k,-13) are collinear. This problem involves finding the coordinates of a point if it is collinear with the other given points. they will lie on the same line, Learn Science with Notes and NCERT Solutions. {/eq}, Become a Study.com member to unlock this (ii) (8, 1), (k, 4), (2, 5) 2k = 8 Login to view more pages. Solved Questions. Here, we have x 1 = K, fy 1 = 3. x 2 = 6, y 2 = -2. and x 3 = -3, y 3 = 4. (x_1,y_1) , (x_2, y_2) Ex 7.3 , 2 (2, 3), (4, a) and (6, –3) Solution : In each of the following find the value of k , for which the points are collinear. The slope of a line joining {eq}\displaystyle Let the given points be A (K. 3), B (6. Sciences, Culinary Arts and Personal i.e. Let the given points be A(7, 2) , B(5, 1) , C(3, k) © copyright 2003-2020 Study.com. All rights reserved. k = 3. Area of ABC = 0 If the above points are collinear, answer! Area of ABC = 0 i.e. So we can either find the value of its unknown coordinate by using the equation of the line or we can equate the slope of the line calculated by these points. 6k = 18 Teachoo is free. He provides courses for Maths and Science at Teachoo. Example 14 Find the value of k if the points A (2, 3), B (4, k) and C (6, –3) are collinear. x3 = 3 , y3 = k x1 = 7 , y1 = 2 7 7k + 5k + 10 9 = 0 {/eq} and... Our experts can answer your tough homework and study questions. 8( 4 + 5) + k( 6) + 2(1 + 4) = 0 2 6k = 10 8 k = ( 18)/( 6) The total cost and the total revenue (in dollars)... 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