The equations to a pair of opposite sides of a parallelogram are and .
The equations to its diagonals are
Step 1: Vertices of a parallelogram.
So the vertices of the parallelogram are .
Step 2: Equation of lines .
Slope of is calculated as
Equation of is calculated as
Slope of is calculated as
Equation of is calculated as
Hence, the equations of the diagonals are and therefore option is the correct answer.