A point A is at a distance of ?29 from the point B(6,-3). Find the coordinates of A , if its ordinate is half of its abscissa. Share with your friends Share 1 Varun.Rawat answered this Let the coordinates of A are Am,nNow, it is given than ordinate of A is half of its abscissa, thenm = 2nSo, coordinates of A are A2n,nNow, B6, -3 is the given point.Now, AB = 29 units⇒2n-62 + n+32 = 29⇒2n-62 + n+32 = 29⇒4n2 + 36 - 24n + n2 + 9 + 6n = 29⇒5n2 - 18n + 16 = 0⇒5n2 - 10n - 8n + 16 = 0⇒5nn-2 - 8n-2 = 0⇒5n-8n-2 = 0⇒5n-8 = 0 or n-2 = 0⇒n = 85 or n = 2When n = 85, then m = 165When n = 2, then m = 4So, coordinates of A are either 4, 2 or 165, 85 1 View Full Answer Jegannathan Anandaraman answered this Hello Vaishnavi, let the point A be (2 a, a) as it is given that ordinate (y) is half of abscissa (x). B is (6,-3) So AB^2 = (√29)^2 = (2a - 6)^2 +(a+3)^2 = 4a^2 - 24 a + 36 + a^2 + 6a + 9 = 5a^2 - 18 a + 45 OR 5 a^2 - 18 a + 45 - 29 = 5 a^2 - 18 a + 16 = 0 Factored as 5a^2 -10a - 8a + 16 = 0 5a(a-2) -8(a -2) = 0 ==> (a-2)(5a - 8) = 0 So a = 2 or a = 8/5 Hence A would be either (4,2) or (16/5 ,8/5) -1
