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Example 3 Given figure shows the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A(3, 1), B(6, 4) and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer. If Ashima, Bharti & Camella are seated in a line, then points A, B & C must be collinear i.e. AB + BC = AC We Find AB , BC & AC using distance formula Finding AB x1 = 3 , y1 = 1 x2 = 6 , y2 = 4 AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((6 −3)2+(4 −1)2) = √((3)2+(3)2) = √(2(3)2) = (√2)3 = 3√𝟐 Finding BC x1 = 6 , y1 = 4 x2 = 8 , y2 = 6 BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((8 −6)2+(6 −4)2) = √((2)2+(2)2) = √(2(2)2) = (√2)2 = 2√𝟐 Finding AC x1 = 3, y1 = 1 x2 = 8, y2 = 6 AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((8 −3)2+(6 −1)2) = √((5)2+(5)2) = √(2(5)2) = (√2)5 = 5√𝟐 Hence AB = 3√2, BC = 2√2, AC = 5√2 Now, AB + BC = 3√2 + 2√2 = 5√2 = AC So, points A, B & C are collinear Hence, Ashima, Bharti and Camilla are seated in a line

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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 and Computer Science at Teachoo