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 A B=√(10) and the points A and C lie on the line 3 y=2 x+1, then 2(α+β+γ+δ) is equal to

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 31 Jan, Morning shift · Q5622

JEE Main 202431 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let

\alpha, \beta, \gamma, \delta \in \mathbb{Z}

and let

A(\alpha, \beta), B(1,0), C(\gamma, \delta)

and

D(1,2)

be the vertices of a parallelogram

\mathrm{ABCD}

. If

A B=\sqrt{10}

and the points

\mathrm{A}

and

\mathrm{C}

lie on the line

3 y=2 x+1

, then

2(\alpha+\beta+\gamma+\delta)

is equal to