Check sibling questions

Slide11.JPG

Slide12.JPG
Slide13.JPG Slide14.JPG Slide15.JPG Slide16.JPG Slide17.JPG


Transcript

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

Ask a doubt (live)
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.