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

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

Accepted Answer

Given the points of B and D are $(\alpha,\beta)$ and $(\gamma,\delta)$ and mid point of A and C is $( - 1, - 2)$

So $\frac{\alpha + \gamma}{2} = - 1$ and $\frac{\beta + \delta}{2} = - 2$

$$|\alpha + \gamma + \beta + \delta| = 6$$

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