How do you explain why perpendicular lines have negative reciprocated slopes?

manpreet Best Answer 3 years ago

For my purposes, I am interested mostly in a medium-sized liberal art college setting. My students have mostly seen this before, but it is not something they understand. When discussing parallel lines, I have them try to find a point of intersection, fail to find such a point, and conclude that the lines never meet, which I think is convincing.

I am trying to find ways that they can convince themselves that two lines with negative reciprocated slopes are perpendicular. Do you have a method that you like?

(also: not sure how to tag this question)