Question:
Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to $7x-y=14$. Find $|\alpha+\beta+\gamma+\delta|$.
Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to $7x-y=14$. Find $|\alpha+\beta+\gamma+\delta|$.
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Midpoint of diagonals coincides in parallelograms.
Updated On: Feb 5, 2026
- 6
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The Correct Option is A
Solution and Explanation
Diagonals bisect at M $(-1, -2)$.
Sum of coordinates of A + C = $(1-3) + (2-6) = -2 -4 = -6$.
In a rhombus (parallelogram), $x_A+x_C = x_B+x_D$ and $y_A+y_C = y_B+y_D$.
$\alpha + \gamma = -2$.
$\beta + \delta = -4$.
Sum = $-6$. Magnitude is 6.
No need to find coordinates explicitly.
Sum of coordinates of A + C = $(1-3) + (2-6) = -2 -4 = -6$.
In a rhombus (parallelogram), $x_A+x_C = x_B+x_D$ and $y_A+y_C = y_B+y_D$.
$\alpha + \gamma = -2$.
$\beta + \delta = -4$.
Sum = $-6$. Magnitude is 6.
No need to find coordinates explicitly.
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