Place the intersection of the diagonals in the origin.
Example Solution:
Practice makes perfect
In the examples mentioned in the question, one vertex of the parallelogram was placed in the origin and one side was placed on the x-axis. We are asked to position a parallelogram on the coordinate plane differently. Let's place the intersection of the diagonals in the origin.
According to Theorem 6.7, the diagonals of a parallelogram bisect each other, so the vertices are in symmetrical position relative to the origin. We can use this observation to label the vertices. We need to make sure that the coordinates of opposite vertices are opposites of each other.
