CBSE Class 12 Sample Paper for 2025 Boards
You are here
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Feb. 12, 2025 by Teachoo
Transcript
Question 6 If the points (𝑥_1,𝑦_1 ),(𝑥_2,𝑦_2 ) and (𝑥_1+𝑥_2,𝑦_1+𝑦_2 ) are collinear, then 𝑥_1 𝑦_2 is equal to (A) 𝑥_2 𝑦_1 (B) 𝑥_1 𝑦_1 (C) 𝑥_2 𝑦_2 (D) 𝑥_1 𝑥_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 ∆ = 1/2 |■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 ∆ = 1/2 |■8(𝑥_1&𝑦_1&1@𝑥_2&𝑦_2&1@𝑥_1+𝑥_2&𝑦_1+𝑦_2&1)| ∆ = 1/2[𝑥_1 (𝑦_2 × 1−(𝑦_1+𝑦_2 )× 1) − 𝑦_1 (𝑥_2 ×1 −(𝑥_1+𝑥_2 )×1) +1(𝑥_2 ×(𝑦_1+𝑦_2 )−(𝑥_1+𝑥_2 )×𝑦_2 ) ] ∆ = 1/2[𝑥_1 (𝑦_2 −𝑦_1−𝑦_2 ) − 𝑦_1 (𝑥_2 −𝑥_1−𝑥_2 ) + 1(𝑥_2 𝑦_1+𝑥_2 𝑦_2−𝑥_1 𝑦_2−𝑥_2 𝑦_2 ) ] ∆ = 1/2[−𝑥_1 𝑦_1+𝑥_1 𝑦_1+𝑥_2 𝑦_1−𝑥_1 𝑦_2] ∆ = 1/2[𝑥_2 𝑦_1−𝑥_1 𝑦_2] Putting Area of Triangle = ∆ = 0 0 = 1/2[𝑥_2 𝑦_1−𝑥_1 𝑦_2] 0 = 𝑥_2 𝑦_1−𝑥_1 𝑦_2 𝑥_1 𝑦_2=𝒙_𝟐 𝒚_𝟏 So, the correct answer is (A)
