Straight Lines
Properties of Parallelogram
JEE Main 2019
Grade 11
Question:
Two sides of a parallelogram are along $x + y = 3$ and $x - y + 3 = 0$. If the diagonals intersect at $(2, 4)$, then one of its vertices is:
(1) $(3, 6)$
(2) $(1, 2)$
(3) $(0, 3)$
(4) $(2, 6)$
Step-by-Step Solution
Key Concept: Find the vertex $A$ common to both given sides. Use the midpoint property: if the diagonals of the parallelogram bisect each other, the opposite vertex $C$ can be found from the midpoint condition, and then find $B$ or $D$ on the given sides.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)