Definition of a Parallelogram
How to solve the definition of a parallelogram problems: example, and its solution (2 ways).
A parallelogram is a quadrilateral
whose two pairs of opposite sides are parallel.
By the definition of a parallelogram,
OR // PQ.
So their slopes are the same.
This means the changes of the coordinates
in OR and PQ are the same: (+6, +2).
So Q(a, b) = (1 + 6, 4 + 2).
Solving this way is easier than setting
(slope of OR) = (slope of PQ).
Example: Another Solution
Of course you can use the other pair of parallel lines:
OP and RQ.
Their slopes are the same.
So the changes of the coordinates
in OP and RQ are the same: (+1, +4).
So Q(a, b) = (6 + 1, 2 + 4).
The answer is the same.