Question: Plot the points $P(0, 3)$, $Q(2, 2)$, and $R(5, 3)$ on a coordinate plane. Where should the point $S$ be located so that the figure $PQRS$ is a parallelogram? Write a brief description of the steps you took and your reasons for taking them.
Solution given in the site:
My question: I believe that the method used (equating the slopes since the sides are parallel) is wrong because of this. Shouldn't the reasoning be this?
There are more than one ways to find the fourth point of a supposed-to-be parallelogram.
Finding it via slopes is a formal and proper method but is NOT the fastest/efficient method. This can be seen from two of the answers provided. However, those methods require some geometrical knowledge and reasoning before one can choose the right tool (like finding the midpoints instead) to start with.
Unfortunately, co-ordinate geometry is basically about slopes and slope-calculating becomes one of the basic and well learnt tools for a learner. That is to say, finding that fourth point via slope-calculating is most likely the tempted try.