Read the text to find the answer.
Step-by-step explanation:
Using a Point on the Given Line:
If you're asked to create perpendicular lines and you're given a line and a point that lies on that line, like point A here, here are the steps to do that. The first thing you want to do is grab your compass. And we're going to make some arcs that intersect the given line. So it really doesn't matter what width your compass is at, as long as it's somewhere within the given line. You want to make sure that these arcs intersect. So put your endpoint on A and swing that arc. We're going to do the same thing on the other side. Now what we want to do is use these two intersection points to create some more arcs above and below point A. So you might want to just mark them off so you know where to put your compass exactly. And then you want to open the compass up a little bit more maybe. You just want to make sure that it's wide enough so that when you create an arc up here [above the given line] from this intersection point [on the line to the left] and again from this one [on the line to the right], that they intersect. So if it's not open wide enough they may not intersect. You need them to intersect. So let's go ahead and start here with the first one on the left. I'm going to swing an arc above, and then again below, point A. I want to do the same thing to the intersection point over here on the right. Remember, we want to make sure that they intersect. They go above and below. Here are the two points [intersections of the arcs above and below the line] that you need to create that perpendicular line. Right there and right there [intersections of the arcs above and below the line] and that line's going to go right through point A. And because we want the lines to be perpendicular, we want the lines to intersect at a 90-degree angle. So go ahead and line up those points and there we go. We can say that this new line intersects the given line at a 90-degree angle, which means you've just created perpendicular lines.
Using a Point Not on a Line:
An instructor is shown in front of a whiteboard. The instructor uses the following steps to construct perpendicular lines through an external point.
When you're asked to construct perpendicular lines and you're given one of those lines and a point that's not on the line, here are the steps you're going to take to do that. You're going to need your compass first. And you're going to want to open it up so that the compass is wider than the distance from the given point to the given line. So I need to open this up a little bit, I think right about there, let me make sure. Okay, so see it opens up and comes down below the line. And you need it to come below the line because you need to mark two arcs. [creates arcs from the point that intersect the line] Okay, so now these two arcs are the same distance from point A, because I kept one side of my compass on that point. Now what we need is to use these two intersection points to create two more arcs down here. Once we have those two arcs, we'll have another point that we can connect with point A, and that line should be perpendicular to the given line. So let's just mark these out, so we know where to put the compass. It doesn't have to be at the same width that you used originally, or you can leave it, so why change it, right? So I'm just going to leave it at that same width and I'm going to mark an arc down here [an arc below the line drawn from the intersection on the left side of the line]. Remember, make sure you go far enough so that they intersect. I'm going to come over here and mark another one [an arc below the line drawn from the intersection on the right side of the line and intersecting the previous arc]. And that's what I want to see, that intersection point. So now I have two points that I can connect and I will have perpendicular lines. So now I've created a second line through point A that's perpendicular to the given line. Remember, that means that it crosses at a 90-degree angle.
