Let A (1,2) and C (-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD an BC are parallel to the line 7 x - y =14 . If B (α, β) and D (γ, δ) are the other two vertices, then α+β+γ+δ is equal to :

Mathematics · Straight lines

JEE Main 2026 — 23 January, Evening Shift — Question 4

Let $\mathrm{A}(1,2)$ and $\mathrm{C}(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD an BC are parallel to the line $7 \mathrm{x}-\mathrm{y}=14$ . If $\mathrm{B}(\alpha, \beta)$ and $\mathrm{D}(\gamma, \delta)$ are the other two vertices, then $|\alpha+\beta+\gamma+\delta|$ is equal to :

Option A:
9
Option B:
3
Option C:
6
Correct
Option D:
1

Answer: C

Step-by-step solution

Midpoint of A and C has coordinates $\left(\frac{1+(-3)}{2}, \frac{2+(-6)}{2}\right) = (-1,-2)$ . In a rhombus, diagonals bisect each other, so the midpoint of BD is also $(-1,-2)$ . Thus $\frac{\alpha+\gamma}{2} = -1 \Rightarrow \alpha+\gamma = -2$ and $\frac{\beta+\delta}{2} = -2 \Rightarrow \beta+\delta = -4$ . Hence $\alpha+\beta+\gamma+\delta = (-2)+(-4) = -6$ . Therefore $|\alpha+\beta+\gamma+\delta| = 6$ .

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Pair of Straight Lines

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Answer: C

Step-by-step solution

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