Question

If \[ x+y-2=0 \] and \[ 2x-y-1=0 \] represent two adjacent sides of a parallelogram and \[ x+4y-14=0 \] represents one of its diagonals, then one of the vertices of the parallelogram is

• A. \(\left(0,\dfrac72\right)\)
• B. \((-2,3)\)
• C. \((-1,6)\)
• D. \((2,-4)\)

Hint:

To solve parallelogram problems:
• Find the common vertex by solving the equations of adjacent sides.
• Use the fact that the diagonals bisect each other.
• The opposite vertex always lies on the given diagonal.

Answer 1

The Correct Option is C