This question is similar Chapter 4 Class 12 Determinants - Ex 4.2

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https://www.teachoo.com/3229/690/Ex-4.3--2---Show-that-A-(a---b---c)--B-(b-c---a)--C-(c-a---b)/category/Ex-4.3/

 

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Question 6 If the points (π‘₯_1,𝑦_1 ),(π‘₯_2,𝑦_2 ) and (π‘₯_1+π‘₯_2,𝑦_1+𝑦_2 ) are collinear, then π‘₯_1 𝑦_2 is equal to (A) π‘₯_2 𝑦_1 (B) π‘₯_1 𝑦_1 (C) π‘₯_2 𝑦_2 (D) π‘₯_1 π‘₯_2Three point are collinear if they lie on some line 𝑖.𝑒. They do not form a triangle ∴ Area of triangle = 0 We know that Area of triangle is given by βˆ† = 1/2 |β– 8(x1&y1&1@x2&y2&1@x3&y3&1)| Here, x1 = x1, y1 = y1 x2 = x2, y2 = y2, x3 = x1 + x2, y3 = y1 + y2 Putting values βˆ† = 1/2 |β– 8(π‘₯_1&𝑦_1&1@π‘₯_2&𝑦_2&1@π‘₯_1+π‘₯_2&𝑦_1+𝑦_2&1)| βˆ† = 1/2[π‘₯_1 (𝑦_2 Γ— 1βˆ’(𝑦_1+𝑦_2 )Γ— 1) βˆ’ 𝑦_1 (π‘₯_2 Γ—1 βˆ’(π‘₯_1+π‘₯_2 )Γ—1) +1(π‘₯_2 Γ—(𝑦_1+𝑦_2 )βˆ’(π‘₯_1+π‘₯_2 )×𝑦_2 ) ] βˆ† = 1/2[π‘₯_1 (𝑦_2 βˆ’π‘¦_1βˆ’π‘¦_2 ) βˆ’ 𝑦_1 (π‘₯_2 βˆ’π‘₯_1βˆ’π‘₯_2 ) + 1(π‘₯_2 𝑦_1+π‘₯_2 𝑦_2βˆ’π‘₯_1 𝑦_2βˆ’π‘₯_2 𝑦_2 ) ] βˆ† = 1/2[βˆ’π‘₯_1 𝑦_1+π‘₯_1 𝑦_1+π‘₯_2 𝑦_1βˆ’π‘₯_1 𝑦_2] βˆ† = 1/2[π‘₯_2 𝑦_1βˆ’π‘₯_1 𝑦_2] Putting Area of Triangle = βˆ† = 0 0 = 1/2[π‘₯_2 𝑦_1βˆ’π‘₯_1 𝑦_2] 0 = π‘₯_2 𝑦_1βˆ’π‘₯_1 𝑦_2 π‘₯_1 𝑦_2=𝒙_𝟐 π’š_𝟏 So, the correct answer is (A)

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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.