Straight Lines
Parallelogram — Distance from Diagonal
nta_pyq_2023_apr
Grade 11
Question:
Adjacent sides of parallelogram $ABCD$: $2x-3y=-23$, $5x+4y=23$. Diagonal $AC$: $3x+7y=23$. If $d$ is distance of $A$ from other diagonal $BD$, then $50d^2$ is equal to ______________
Step-by-Step Solution
Key Concept: Find $A$ (intersection of adjacent sides), then equation of $BD$ using parallelogram property (diagonals bisect each other). Compute distance.
$50d^2=529$.
Correct Answer: 529