Let α, β, γ, ∈ Z and let A (α, β), B (1, 0), C(γ, ) 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 + ) is equal to

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Correct answer: D. 8

Plotting the diagram of the given data we get,

Let α, β, γ, ∈ Z and let A (α, β), B (1, 0), C(γ, ) and D(1, 2) be the vertices of a parallelogram ABCD . If AB = 10

We know that diagonals of a parallelogram bisect each other.

$⇒ \text{Mid-point of}AC = \text{Mid-point of}BD$

$⇒ \left(\dfrac{\alpha + \gamma}{2}, \dfrac{\beta + \delta}{2}\right) = \left(\dfrac{1 + 1}{2}, \dfrac{0 + 2}{2}\right)$

$⇒ \left(\dfrac{\alpha + \gamma}{2}, \dfrac{\beta + \delta}{2}\right) = \left(1, 1\right)$

$⇒ \alpha + \gamma = 2, \beta + \delta = 2$

$⇒ 2\left(\alpha + \gamma + \beta + \delta\right) = 8$

Let α, β, γ, ∈ Z and let A (α, β), B (1, 0), C(γ, ) and D(1, 2) be...

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