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Ex 7.1, 5 In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct. As seen from the figure, four points are A(3, 4) , B(6, 7) C(9, 4) , D(6, 1) In a square, All sides are equal All diagonals are equal Hence, we have to prove AB = BC = CD = AD and AC = BD Finding sides using Distance Formula Finding AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(7 −4)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding BC BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(4 −7)2) = √((3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding CD CD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −9)2+(1 −4)2) = √((−3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding AD AD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(1 −4)2) = √((3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Similarly finding the diagonals Finding AC AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((9 −3)2+(4−4)2) = √((6)2+(0)2) = √((6)2) = 6 Finding BD BD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −6)2+(1 −7)2) = √((0)2+(−6)2) = √((6)2) = 6 Now since AB = BC = CD = AD = 3√2 & AC = AD = 6 Since the sides of ABCD are equal and diagonals are equal So, ABCD is a square Therefore, Champa is correct. Now since AB = BC = CD = AD = 3√2 & AC = AD = 6 Since the sides of ABCD are equal and diagonals are equal So, ABCD is a square Therefore, Champa is correct.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.