Endeavoring to bring some flavor of "real world" application to each topic in my community college precalculus class, I find myself struggling to provide some non-geometric motivation for perpendicular lines.
Applications of parallel lines are a dime-a-dozen, as the idea of rate-of-change is easy for students to discuss when there are units involved. The discussion of the relevant units makes the conversation meaningful.
Now, is there some level-appropriate, non-geometric application of perpendicularity? I am having trouble thinking of something that doesn't strictly rely on the angle between the functions ("find the equations for the sides of this square"), tangent lines (e.g. finding the gradient), or a special case with the units ignored ("this thing goes up by 1 each year, and the other thing goes down by 1 each year").
Do you have a go-to example of a non-geometric application of perpendicularity for precalculus students? In your example, do the units tell something useful? If so, I'd love to hear about it.
Incidentally, here's what I'm thinking of as an easy-to-build application of parallel functions for my students:
- Two people begin working at the same job, and each year they will both see a 2000 dollar-per-year raise. Person A comes with experience, beginning at 55000 dollars per year, and person B starts at 45000 dollars per year.