JEE Main 2026 — Jan 23, Shift 2 — Mathematics solution

JEE Main2026Jan 23, Shift 2Mathematics

Let $A (1, 2)$ and $C (- 3, - 6)$ be two diagonally opposite vertices of a rhombus, whose sides $A D$ and $B C$ 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 :

Solution

In a rhombus the diagonals bisect each other, so the midpoint of $B D$ equals the midpoint of $A C$ :

Midpoint of $A C = (\frac{1 + ( - 3 )}{2}, \frac{2 + ( - 6 )}{2}) = (- 1, - 2)$ .

Hence $\frac{α + γ}{2} = - 1$ and $\frac{β + δ}{2} = - 2$ .

$α + γ = - 2$ , $β + δ = - 4$ .

$∣ α + β + γ + δ ∣ = ∣ - 2 - 4∣ = 6$ .

(The condition on side direction fixes the individual vertices uniquely, but is not needed for this sum.)

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