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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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:
Solution
Given the points of $B$ and $D$ are $(\alpha,\beta)$ and $(\gamma,\delta)$
Midpoint of $AC = (-1,-2)$
$\frac{\alpha + \gamma}{2} = -1,\quad \frac{\beta + \delta}{2} = -2$
$\Rightarrow \alpha + \gamma = -2,\quad \beta + \delta = -4$
$\Rightarrow |\alpha + \beta + \gamma + \delta| = |-6| = 6$
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