This question is similar Chapter 4 Class 12 Determinants - Ex 4.2
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CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 by Teachoo
Question 6 If the points (π₯_1,π¦_1 ),(π₯_2,π¦_2 ) and (π₯_1+π₯_2,π¦_1+π¦_2 ) are collinear, then π₯_1 π¦_2 is equal to (A) π₯_2 π¦_1 (B) π₯_1 π¦_1 (C) π₯_2 π¦_2 (D) π₯_1 π₯_2Three point are collinear if they lie on some line π.π. They do not form a triangle β΄ Area of triangle = 0 We know that Area of triangle is given by β = 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 β = 1/2 |β 8(π₯_1&π¦_1&1@π₯_2&π¦_2&1@π₯_1+π₯_2&π¦_1+π¦_2&1)| β = 1/2[π₯_1 (π¦_2 Γ 1β(π¦_1+π¦_2 )Γ 1) β π¦_1 (π₯_2 Γ1 β(π₯_1+π₯_2 )Γ1) +1(π₯_2 Γ(π¦_1+π¦_2 )β(π₯_1+π₯_2 )Γπ¦_2 ) ] β = 1/2[π₯_1 (π¦_2 βπ¦_1βπ¦_2 ) β π¦_1 (π₯_2 βπ₯_1βπ₯_2 ) + 1(π₯_2 π¦_1+π₯_2 π¦_2βπ₯_1 π¦_2βπ₯_2 π¦_2 ) ] β = 1/2[βπ₯_1 π¦_1+π₯_1 π¦_1+π₯_2 π¦_1βπ₯_1 π¦_2] β = 1/2[π₯_2 π¦_1βπ₯_1 π¦_2] Putting Area of Triangle = β = 0 0 = 1/2[π₯_2 π¦_1βπ₯_1 π¦_2] 0 = π₯_2 π¦_1βπ₯_1 π¦_2 π₯_1 π¦_2=π_π π_π So, the correct answer is (A)