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Solution


Q.

Let α,β,γ, δ∈Z and let A(α,β),B(1,0),C(γ,δ) and D(1, 2) be the vertices of a parallelogram ABCD. If AB=10 and the points A and C lie on the line 3y = 2x + 1, then 2(α+β+γ+δ) is equal to          [2024]
1 12  
2 10  
3 8  
4 5  

Ans.

(3)

Givem, A(α, β), B(1, 0), C(γ, δ) and D(1, 2).

Using mid point Formula.

α + γ=2

β + δ = 2

So, α + β + γ + δ = 2 + 2

α + β + γ + δ = 4

∴   2(α + β + γ + δ) = 2(4) = 8.