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Ex 7.1, 3 Determine if the points (1, 5), (2, 3) and (–2, – 11) are collinear. Let the 3 points be A (1, 5), B (2, 3) & C (−2, −11) Collinear points are points which fall on the same line There are three cases possible Case 1 A, B & C are collinear if AB + BC = AC Case 2 A, B & C are collinear if BA + AC = BC Case 3 A, B & C are collinear if BC + CA = BA Finding AB A (1, 5) & B (2, 3) x1 = 1, y1 = 5 x2 = 2, y2 = 3 AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 2 −1)2+(3 −5)2) = √((1)2+(−2)2) = √(1+4) = √𝟓 Finding BC B (2, 3) & C (−2, −11) x1 = 2, y1 = 3 x2 = −2, y2 = −11 BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( −2 −2)2+(−11 −3)2) = √((−4)2+(−14)2) = √(16+196) = √212 = √(2×2×53) = 2√𝟓𝟑 Finding AC A (1, 5), B (2, 3) & C (−2, −11) x1 = 1 , y1 = 5 x2 = −2, y2 = −11 AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( −2 −1)2+(−11 −5)2) = √((−3)2+(−16)2) = √(9+256) = √𝟐𝟔𝟓 Hence, AB = √5, BC = 2√53, AC = √265 Now we check all the three cases Case 1 AB + BC = AC L.H.S ≠ R.H.S Hence Case 1 is not true Case 2 BA + AC = BC Case 3 BC + CA = BA Since all 3 cases are not true, ∴ Points are not collinear

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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.