Straight Lines
Properties of Parallelogram
JEE Main 2021
Grade 11
Question:
Two sides of a parallelogram are along the lines $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one diagonal is $11x + 7y = 9$, the equations of the other two sides are:
(1) $4x + 5y = 9$ and $7x + 2y = 9$
(2) $4x+5y+9 = 0$ and $7x+2y+9 = 0$
(3) $2x + 5y = 9$ and $7x + 4y = 9$
(4) $4x - 5y = 9$ and $7x - 2y = 9$
Step-by-Step Solution
Key Concept: The two given sides pass through the origin $O$, so $O$ is a vertex. Find the other two vertices by intersecting the diagonal with each side, then write the sides parallel to the given ones through those vertices.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)