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Ex 11.2, 3 Verify the following: (i) (0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle. Let points be A (0, 7, – 10) , B (1, 6, – 6) & C (4, 9, – 6) If any 2 sides are equal, it will be an isosceles triangle Lets calculate AB, BC, AC Calculating AB A (0, 7, – 10) B (1, 6, – 6) AB = √((x2−x1)2+(y2−y1)2+(z2 −z1)2) Here, x1 = 0, y1 = 7, z1 = – 10 x2 = 1, y2 = 6, z2 = – 6 AB = √((1−0)2+(6−7)2+(−6+10)2) = √((1)2+(−1)2+(4)2) = √(1+1+16) = √18 = 3√2 Calculating BC B (1, 6, –6) C (4, 9, –6) BC = √((x2−x1)2+(y2−y1)2+(z2 −z1)2) Here x1 = 1, y1 = 6, z1 = – 6 x2 = 4, y2 = 9, z2 = – 6 BC = √((4−1)2+(9−6)2+(−6−(−6))2) = √((3)2+(3)2+(−6+6)2) = √(9+9+0) = √18 Since AB = BC ∴ 2 Sides are equal Hence, ABC is an isosceles triangle Note: We don’t need to calculate AC

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.