Ex 7.1, 3 - Chapter 7 Class 10 Coordinate Geometry
Last updated at April 16, 2024 by Teachoo
Checking points collinear or not
Checking points collinear or not
Last updated at April 16, 2024 by Teachoo
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