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Ex 7.1, 4 Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle. In an isosceles triangle, any 2 of the 3 sides are equal. Let the three points be P(5, −2), Q(6, 4) & R(7, −2) In order to be isosceles, Either PQ = PR or PQ = QR or PR = QR We calculate the value of PQ, QR & PR by distance formula Calculating PQ PQ = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −5)2+(4 −(−2))2) = √(12+(6)2) = √(1+36) = √37 Calculating QR QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −6)2+(−2 −4)2) = √(12+(−6)2) = √(1+36) = √37 Calculating PR PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −5)2+(−2 −(−2))2) = √(22+(−2+2)2) Calculating QR QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −6)2+(−2 −4)2) = √(12+(−6)2) = √(1+36) = √37 Calculating PR PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −5)2+(−2 −(−2))2) = √(22+(−2+2)2) Calculating QR QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −6)2+(−2 −4)2) = √(12+(−6)2) = √(1+36) = √37 Calculating PR PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 7 −5)2+(−2 −(−2))2) = √(22+(−2+2)2) = √(2^2+0^2 ) = √(2^2 ) = 2 Hence, PQ = √37, QR = √37, PR = 2 Since PQ = QR It satisfies the condition of isosceles triangle Hence, PQR is an isosceles triangle

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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.