And what does that mean? Well, you're going down 1 unit in the y-direction for every 1 unit you move in the x-direction. This time, you start your journey with a slope of -1. You start from point B, which is at coordinates (a,0), and you head towards point D, located at (0,a). Now, let's think about line BD as another road trip. Yeah, math can be weird sometimes, but hey, it keeps things interesting. How do we know that? Well, the math gods tell us that in order for two lines to be perpendicular, the product of their slopes must be -1. And guess what? It's perpendicular to AC. You're cruising along nicely, going up 1 unit in the y-direction for every 1 unit you move in the x-direction.īut wait! The diagonal BD connects points B and D. So, let's say you start driving with a slope of 1. Now, the slope of a line is like the speed at which you're driving on that road trip. You start from point A, which is at the origin (0,0), and head towards point C, which has coordinates (a,a). We're going to use coordinate geometry to tackle this problem.įirst, let's find the slopes of the two diagonals. Now, we have our square with vertices A, B, C, and D. Alright, listen up folks, we're about to prove that the diagonals of a square are perpendicular.