 So the next step in our Thiessen polygon method is going to be to find ortho-centers and ortho-centers of the Delaunay triangles that we created earlier. So in order to be ready for this step, you need a map with your Delaunay triangulation and with each of the segments, all three in each triangle, that have been bisected, split in half. And if you go extended them so that you can see the perpendicular, that will also be valuable. So, what we have to do for each of these triangles, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, there are twelve triangles here. For each of these triangles, we're going to try to find the ortho-center. The ortho-center of each triangle is the location where the lines that are perpendicular to each side of the triangle meet. And because each of these lines are perpendicular bisectors, if we extend those three, they will always meet at one point. And what we need to do for each of these is to locate the ortho-centers for all twelve of my triangles. So in some of these cases, those centers may not be on the actual map. If so, we do our best to approximate where they are, but it's okay for some of them if we were unable to locate them because they're not actually on the plane. Let's go ahead and see if we can locate the ortho-centers for this triangle over here on the left. If I take a look at that triangle, you see that there are three sides, and each of those three sides has a bisector. I'm going to take a piece of paper, a corner of a piece of paper, line it up so that it's one side is along that line, and the other side is going to create a right angle, and I'm going to line up the point on our bisection point. And from there, I'm going to lightly sketch a line that comes out from there. Why did I go in this direction? Generally, you're going to go in the direction that moves toward the other lines in the triangle, although that will not always necessarily be into the triangle. If I go to this other side of the triangle and do a similar thing, I'll create another point, and notice I actually only need two points here to determine where my ortho-center is. However, it's probably a good idea that I verify or validate that ortho-center by sketching this third perpendicular bisector, and we should see that the three of them meet at a common point or a very close to common point depending on how good my sketching is. So there is my first ortho-center corresponding to this triangle here. I'm going to need to repeat that process for each of the triangles. Let me repeat it for the triangle here. Notice I've already used this particular line and have a perpendicular bisector. It looks to me like it's going to meet very close to where this line is, and this line is the one that I did earlier that I used a compass to sort of create a perpendicular line, so it's fairly easy to extend that line until the three of them meet at their common point. Let me choose one more example here of this long, very thin triangle near the bottom. Notice in that case if I create my perpendicular line along this segment and similarly create a perpendicular line along the other segment, it's readily apparent that these lines are not going to end up intersecting on the page. We just do our best to note that there is an ortho-center off there somewhere and we will have to consider that later on. So your next task is to generate ten more or actually nine more ortho-centers, one for each of the triangles.