00:01
To begin finding the distance between these two points, let's first decide that f will be our first point, and g will be our second.
00:09
We can then use this information to fill in our formula, which is written over here.
00:13
So let's start by identifying x2.
00:17
X2 is the x that goes with our second point, so x2 is zero.
00:22
We're going to subtract from that x1, which is three -fifths.
00:29
This will eventually be squared, so let's add that.
00:32
Now let's look at our y's.
00:35
Y2 is 3 minus y1, which is 0, squared.
00:45
Next, we're going to look at our zs.
00:47
So we have z2, which is 0, minus z1, which is 4 5ths.
00:54
And again, this difference will be squared.
00:57
At the end, all of this will be square rooted.
00:59
But first let's figure out what we will be actually square rooting.
01:02
0 minus 3 5ths is negative 3 5ths.
01:09
Now remember, this will be squared.
01:13
3 minus 0 is 3.
01:14
This will also be squared, and 0 minus 4 fifths is negative 4 fifths, which of course will be squared.
01:25
Now remember, when you are squaring a fraction, you're multiplying that fraction by itself.
01:30
So when we're doing negative 3 fifth squared, we're doing negative 3 fifths times negative 3 fifths.
01:36
Negative 3 fifths times negative 3 fifths is 9 20 fifths, because we multiply across the top and across the bottom.
01:46
3 squared is 9, and then negative 4 fifths.
01:51
Squared is 16 .25s for the same reason as my first point.
01:58
Now take a look what we have here.
02:00
We have 9 .25s and 16 .25s.
02:04
9 plus 16.
02:05
25.
02:06
So what we really have is 25, 25ths plus 9.
02:16
Well, 25 25ths is 1 and 1 plus 9 is of course 10.
02:24
Now we're not finished yet.
02:26
We have to take the square root of this because the formula for distance requires us to take the square root of everything.
02:33
So the distance between these two points is the square root of 10...