Question Video: Finding the Distance between Two Points in a Word Problem Mathematics • 6th Grade

James and Daniel are two friends who go to the same school. James’s room is located at (−5, 6), Daniel’s room at (−5, −4), and the band room at (4, −4). How far is James’s room from Daniel’s? What is the distance between Daniel’s room and the band room?

03:18

Video Transcript

James and Daniel are two friends who go to the same school. James’s room is located at negative five, six; Daniel’s room at negative five, negative four; and the band room at four, negative four. How far is James’s room from Daniel’s? What is the distance between Daniel’s room and the band room?

So what we’re gonna begin with is this first part of the question. So what we want to find out is how far James’s room is from Daniel’s. So what we’ve got are two points, and these are the locations of James’s and Daniel’s room. So I’m gonna call James’s room 𝐽 — so this is at negative five, six — and Daniel’s room 𝐷 — and this is at negative five, negative four.

Well, the key here when we take a look at both of these points is the fact that their 𝑥-coordinate is the same. They both have the 𝑥-coordinate of negative five. And if we take a little look at it on a sketch, we could see that they’d have the same 𝑥-coordinate. So therefore, what it means is that 𝐽 would be vertically above 𝐷. So therefore, the distance from 𝐽 to 𝐷 is just gonna be the difference between our 𝑦-coordinates.

So to calculate this, what we’re gonna do is six minus negative four. Well, if we’ve got six minus negative four, well, if you subtract a negative, it’s the same as adding a positive. So it’s gonna give us six add four, which is gonna be equal to 10.

Okay, so we did this with six minus negative four. But you might be thinking, “Oh, hold on! That was subtracting the 𝑦-coordinate of 𝐷 away from the 𝑦-coordinate of 𝐽. What happens if I did it the other way around?” Well, if we did it the other way around, what we’d have is negative four minus six. Well, negative four minus six is negative 10.

So all we would do is we would disregard the sign in this instance because what we’re looking for is just a distance between two points. So it doesn’t matter if it’s negative 10 or 10. They would both tell us that the distance between the two points is 10.

Okay, so now let’s move on to the second part of the question. So for the second part of the question, what we’re looking at is distance between Daniel’s room and the band room. Well, once again, we’ve got 𝐷, which is gonna be Daniel’s room at negative five, negative four. Then we’ve got the band room, which I’m gonna represent with 𝐵, which is four, negative four.

So once again, we can see that they share a same coordinate. This time, it’s the 𝑦-coordinates. So the 𝑦-coordinates of 𝐷 and 𝐵 are the same cause they’re both negative four. Well, therefore, if we’ve got the two points sharing the same 𝑦-coordinate, then the distance between them is just gonna be the difference between the 𝑥-coordinates.

So what we can do to work this out is we can either count up from negative five to four, which would give us a distance or difference of nine. Or we could work it out from the 𝑥-coordinates. So what we could do is subtract the 𝑥-coordinate of 𝐵 from the 𝑥-coordinate of 𝐷. So in that case, we’d have negative five minus four, which would give us negative nine. But once again, because we’re looking at distance, then we want the modulus of this. Or, in other words, we don’t want to regard the sign. So therefore, it’s just gonna be nine units.

So therefore, we can say that the distance between Daniel’s room and the band room is nine.

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