Let A(1,2) and C(3,6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7xy=14 If B and are the other two vertices, th

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Solution

Q.
Let A(1, 2) and C(−3, −6) be two diagonally opposite vertices of a rhombus, whose sides AD and 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. [2026]

1 6

2 1

3 3

4 9

Ans.
(1)

[IMAGE 194]

$Given the points of B and D are (α, β) and (γ, δ)$ $and midpoint of A and C is (- 1, - 2)$

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

$| α + γ + β + δ |$ $= 6$

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