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.
