Check if the Goal keeper G(-3, 5), Sweeper H(3, 1) and Wing-back K(0,3) fall on a same straight line

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Transcript

Given coordinates G(-3, 5), H(3, 1) and K(0,3) We need to check if they are in same straight line, i.e. we need to check collinear If points G, H, K are collinear, they will lie on the same line, i.e. they will not form triangle Therefore, Area of ∆GHK = 0 Now, finding Area of ∆GHK Area of ∆GHK = 1/2 [ x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) ] Since G(-3, 5), H(3, 1) and K(0, 3) Here x1 = −3, y1 = 5 x2 = 3, y2 = 1 x3 = 0, y3 = 3 Now, Area of ∆GHK = 1/2 [−3(1 – 3) + 3(3 − 5) + 0(5 – 1)] = 1/2 [−3 × −2 + 3 × −2 + 0(5 – 1)] = 1/2 [6 − 6] = 1/2 × 0 = 0 Since Area of ∆GHK = 0 Thus, G, H and K fall on same 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.