Let A(1,2) and C(-3,-6) be two diagonally opp | vedclass

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(C) In a rhombus, the diagonals bisect each other at right angles. Let $O$ be the intersection of diagonals $AC$ and $BD$. The coordinates of $O$ are

Vedclass · Accepted Answer

$6$

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(C) In a rhombus, the diagonals bisect each other at right angles. Let $O$ be the intersection of diagonals $AC$ and $BD$. The coordinates of $O$ are the midpoint of $AC$: $O = \left(\frac{1-3}{2}, \frac{2-6}{2}\right) = (-1, -2)$. Since $O$ is also the midpoint of $BD$, we have: $\frac{\alpha+\gamma}{2} = -1 \implies \alpha+\gamma = -2$ $\frac{\beta+\delta}{2} = -2 \implies \beta+\delta = -4$ We need to find $|\alpha+\beta+\gamma+\delta|$. $|\alpha+\beta+\gamma+\delta| = |(\alpha+\gamma) + (\beta+\delta)| = |-2 + (-4)| = |-6| = 6$.

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 $7x-y=14$. If $B(\alpha, \beta)$ and $D(\gamma, \delta)$ are the other two vertices, then $|\alpha+\beta+\gamma+\delta|$ is equal to:

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