Compare and order absolute values. Absolute value as distance between numbers.
Absolute value to find distance. Video transcript - [Voiceover] Let's say that I have two numbers on a number line. So let me draw a little quick number line right over here. The two numbers on my number line that I care about, the number a and the number represented by b here.
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The way I've drawn it, b is to the right of a on our number line, and by our convention, b is going to be greater than a. So if I were to figure out the distance between a and b, what is this distance going from a, I want to draw a straight line here, this distance going from a to b, so this distance right over there, how would I figure it out?
Well I could just take the larger of these two numbers, which is going to be b, and then subtract out the smaller. So I subtract out a, and I'll be left with this distance. This will give me a positive value. When I want a distance, I just think in terms of a positive value. How far apart are these two things? But I was only able to know to do b minus a because I knew that b was greater than a. This was going to give me a positive value. What if I knew that a was greater than b?
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Well then I would do it the other way around. So let me draw that again. Let me draw another number line right over here.
In this world, in this world, I'm going to make a greater than b. This is b, that is a, and if I wanted to calculate the distance between b and a here, well now I would take the larger of the two, a, remember I want the positive distance here, and then I would subtract out the smaller. I would do a minus b.
Distance between point & line (video) | Khan Academy
Well so here I did b minus a, here I did a minus b, but what if I didn't know which one was greater? If I didn't know whether b or a was greater, what could I do? Well what you could do is just take either a minus b or b minus a and take the absolute value. If you do that, it doesn't matter if you take b minus a or a minus b. It turns out that regardless of whether a is greater than b, or b is greater than a, or they're equivalent, that the absolute value of a minus b is equivalent to the absolute value of b minus a, and this is equivalent, either of these expressions is the distance between these numbers.
I encourage you to play around with the negatives to see if you can factor out some negatives and think about the absolute value.
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It will actually make a lot of sense why this is true. In another video, I might do a little bit more of a rigorous justification for it. But I think the important thing for this video is to see that this is actually true.
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Touch and hold anywhere on the map. You'll see a red pin appear. At the bottom, tap the name of the place. Add the next point or points Move the map so that the black circle, or crosshairs, is on the next point you want to add.