Straight Lines
Rhombus — Other Vertices, |α+β+γ+δ|
nta_pyq_2026_jan
Grade 11
Question:
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
Step-by-Step Solution
Key Concept: Midpoint of $AC$: $M=(-1,-2)$. Slope of $AC=\tfrac{-6-2}{-3-1}=2$. Diagonal $BD\perp AC$: slope $=-1/2$, passes through $M$. $AD$ has slope 7 (parallel to $7x-y=14$).
$|\alpha+\beta+\gamma+\delta|=6$.
Correct Answer: 1