Question Video: Finding the Distance between Two Points given Their Coordinates | Nagwa Question Video: Finding the Distance between Two Points given Their Coordinates | Nagwa

# Question Video: Finding the Distance between Two Points given Their Coordinates Mathematics • Sixth Year of Primary School

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Find the length of 𝐴𝐵.

02:59

### Video Transcript

Find the length of the line segment 𝐴𝐵.

Well, there’re a couple of ways that we can approach this question. So first of all, the first method is to just count the squares between the two points. And that’s because if we join 𝐴 to 𝐵, we’ve got line segment 𝐴𝐵. And if we count the squares between them, it’s gonna be six units. And that’s because each square is one length unit. And what this is is the vertical distance between 𝐴 and 𝐵. So therefore, we could say that the length of the line segment 𝐴𝐵 is six length units.

However, I did say that there was another way that we could look at this. Well, the other way to look at this is to look at the coordinates for each point. So the coordinator of 𝐴 are six, two. And the coordinates of 𝐵 are six, eight. And because they have the same 𝑥-coordinate, this means that we know that they’re in the same vertical plane. So therefore, we know that the distance between them is just gonna be the change in 𝑦, so the change in their 𝑦-coordinates. And the change in their 𝑦-coordinates is just gonna be eight minus two, which is equal to six, so it gives us the same answer.

So this was a nice, simple example to start off. But what we’re gonna have a look at now is another example that involves both the horizontal and vertical distances between points. And so far, we’ve shown a couple of methods to do this. But what we’re gonna do before we have a look at the next example is have a look at the distance between two points formula. So the distance between two points formula is something we can use to find the distance between any two points on our coordinate plane. So let’s consider two points. So the two points we’ve got are 𝐴, which we can denote with 𝑥 sub 𝐴, 𝑦 sub 𝐴, and 𝐵, which is 𝑥 sub 𝐵, 𝑦 sub 𝐵.

Well, in fact, what we can do is find the distance between them by applying the Pythagorean theorem. And that is that we could say the distance between 𝐴 and 𝐵 is equal to the square root of 𝑥 sub 𝐵 minus 𝑥 sub 𝐴 all squared, so the change in 𝑥 all squared, plus 𝑦 sub 𝐵 minus 𝑦 sub 𝐴 all squared, so that’s the change in 𝑦 all squared. And the reason this works is if we imagine two points, said point 𝐴 and point 𝐵, well, then, if we join them together, then what we’d have is a right triangle with the vertical length being the change in 𝑦, so 𝑦 sub 𝐵 minus 𝑦 sub 𝐴, and the horizontal length being the change in 𝑥, 𝑥 sub 𝐵 minus 𝑥 sub 𝐴.

So this method could be used to find the distance between any two points on the coordinate plane. However, we’ve already seen that if we’re looking at horizontal or vertical distances, we can find it using more simple methods. But what we do want to do is demonstrate how this would in fact work for problems that do involve horizontal and vertical distances. So we’re gonna use it in our next example.

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