This question is similar to Chapter 7 Class 10 Coordinate Geometry - Ex 7.1

Please check the Question here

https://www.teachoo.com/1722/524/Ex-7.1--4---Check-whether-(5---2)--(6---4)-and-(7---2)/category/Ex-7.1/

 

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Question 25 Show that the points A(-5,6), B(3, 0) and C(9, 8) are the vertices of an isosceles triangle. In an isosceles triangle, any 2 of the 3 sides are equal. The three points are A(-5,6), B(3, 0) and C(9, 8) In order to be isosceles, Either AB = AC or AB = BC or BC = AC A (−5, 6) B (3, 0) C (9, 8) We calculate the value of AB, BC & AC by distance formula Calculating AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((𝟑 −(−𝟓))𝟐+(𝟎−𝟔)𝟐) = √((3+5) 2+(−6)2) = √(8 2+62) = √(64+36) = √𝟏𝟎𝟎 = √(10^2 ) = 10 Calculating BC BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 9 −3)2+(8 −0)2) = √(62+82) = √(36+64) = √𝟏𝟎𝟎 = √(10^2 ) = 10 Calculating AC AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 9 −(−5))2+(8−6)2) = √((9+5)^2+22) = √(14^2+22) = √(196+4) = √𝟐𝟎𝟎 Hence, AB = 10, BC = 10, AC = √200 Since AB = BC It satisfies the condition of isosceles triangle Hence, Δ ABC is an isosceles triangle

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.