[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.27,0:00:02.47,Default,,0000,0000,0000,,- We are asked what is the distance
Dialogue: 0,0:00:02.47,0:00:05.16,Default,,0000,0000,0000,,between the following points.
Dialogue: 0,0:00:05.16,0:00:08.38,Default,,0000,0000,0000,,Pause this video and see\Nif you can figure it out.
Dialogue: 0,0:00:08.38,0:00:10.43,Default,,0000,0000,0000,,There's multiple ways to think about it.
Dialogue: 0,0:00:10.43,0:00:12.92,Default,,0000,0000,0000,,The way I think about it\Nis really to try to draw
Dialogue: 0,0:00:12.92,0:00:15.80,Default,,0000,0000,0000,,a right triangle where these points,
Dialogue: 0,0:00:15.80,0:00:18.88,Default,,0000,0000,0000,,where the line that connects\Nthese points is the hypotenuse
Dialogue: 0,0:00:18.88,0:00:21.46,Default,,0000,0000,0000,,and then we can just use\Nthe Pythagorean Theorem.
Dialogue: 0,0:00:21.46,0:00:24.22,Default,,0000,0000,0000,,Let me show you what I am talking about.
Dialogue: 0,0:00:24.22,0:00:27.14,Default,,0000,0000,0000,,Let me draw a right triangle, here.
Dialogue: 0,0:00:28.25,0:00:31.26,Default,,0000,0000,0000,,That is the height of my right triangle
Dialogue: 0,0:00:31.26,0:00:34.85,Default,,0000,0000,0000,,and this is the width\Nof my right triangle.
Dialogue: 0,0:00:35.72,0:00:37.77,Default,,0000,0000,0000,,Then the hypotenuse will\Nconnect these two points.
Dialogue: 0,0:00:37.77,0:00:40.44,Default,,0000,0000,0000,,I could use my little\Nruler tool here to connect
Dialogue: 0,0:00:40.44,0:00:44.02,Default,,0000,0000,0000,,that point and that\Npoint right over there.
Dialogue: 0,0:00:45.03,0:00:47.19,Default,,0000,0000,0000,,I'll color it in orange.
Dialogue: 0,0:00:47.19,0:00:49.31,Default,,0000,0000,0000,,There you have it.
Dialogue: 0,0:00:49.31,0:00:50.48,Default,,0000,0000,0000,,There you have it.
Dialogue: 0,0:00:50.48,0:00:53.30,Default,,0000,0000,0000,,I have a right triangle\Nwhere the line that connects
Dialogue: 0,0:00:53.30,0:00:57.36,Default,,0000,0000,0000,,those two points is the\Nhypotenuse of that right triangle.
Dialogue: 0,0:00:57.36,0:00:58.86,Default,,0000,0000,0000,,Why is that useful?
Dialogue: 0,0:00:58.86,0:01:00.80,Default,,0000,0000,0000,,From this, can you pause\Nthe video and figure out
Dialogue: 0,0:01:00.80,0:01:03.54,Default,,0000,0000,0000,,the length of that orange\Nline, which is the distance
Dialogue: 0,0:01:03.54,0:01:06.27,Default,,0000,0000,0000,,between those two points?
Dialogue: 0,0:01:06.27,0:01:09.40,Default,,0000,0000,0000,,What is the length of this red line?
Dialogue: 0,0:01:09.40,0:01:11.57,Default,,0000,0000,0000,,You could see it on this grid, here.
Dialogue: 0,0:01:11.57,0:01:13.35,Default,,0000,0000,0000,,This is equal to two.
Dialogue: 0,0:01:13.35,0:01:15.96,Default,,0000,0000,0000,,It's exactly two spaces, and\Nyou could even think about it
Dialogue: 0,0:01:15.96,0:01:17.39,Default,,0000,0000,0000,,in terms of coordinates.
Dialogue: 0,0:01:17.39,0:01:19.62,Default,,0000,0000,0000,,The coordinate of this point up here
Dialogue: 0,0:01:19.62,0:01:22.04,Default,,0000,0000,0000,,is negative five comma eight.
Dialogue: 0,0:01:23.02,0:01:25.75,Default,,0000,0000,0000,,Negative five comma eight.
Dialogue: 0,0:01:25.75,0:01:29.33,Default,,0000,0000,0000,,The coordinate here is\NX is four, Y is six.
Dialogue: 0,0:01:30.34,0:01:33.82,Default,,0000,0000,0000,,Four comma six, and so\Nthe coordinate over here
Dialogue: 0,0:01:33.82,0:01:37.99,Default,,0000,0000,0000,,is going to have the same\NY coordinate as this point.
Dialogue: 0,0:01:39.49,0:01:41.41,Default,,0000,0000,0000,,This is going to be comma six.
Dialogue: 0,0:01:41.41,0:01:43.13,Default,,0000,0000,0000,,It's going to have the same\NX coordinate as this point.
Dialogue: 0,0:01:43.13,0:01:45.56,Default,,0000,0000,0000,,This is going to be\Nnegative five comma six.
Dialogue: 0,0:01:45.56,0:01:48.36,Default,,0000,0000,0000,,Notice, you're only\Nchanging in the Y direction
Dialogue: 0,0:01:48.36,0:01:50.70,Default,,0000,0000,0000,,and you're changing by two.
Dialogue: 0,0:01:50.70,0:01:53.61,Default,,0000,0000,0000,,What's the length of this line?
Dialogue: 0,0:01:53.61,0:01:55.88,Default,,0000,0000,0000,,You could count it out, one, two, three,
Dialogue: 0,0:01:55.88,0:01:59.17,Default,,0000,0000,0000,,four, five, six, seven, eight, nine.
Dialogue: 0,0:01:59.17,0:02:01.75,Default,,0000,0000,0000,,It's nine, or you could even say hey look,
Dialogue: 0,0:02:01.75,0:02:04.58,Default,,0000,0000,0000,,we're only changing in the X value.
Dialogue: 0,0:02:04.58,0:02:06.19,Default,,0000,0000,0000,,We're going from negative five,
Dialogue: 0,0:02:06.19,0:02:09.08,Default,,0000,0000,0000,,X equals negative five, to X equals four.
Dialogue: 0,0:02:09.08,0:02:11.48,Default,,0000,0000,0000,,We're going to increase by nine.
Dialogue: 0,0:02:11.48,0:02:13.62,Default,,0000,0000,0000,,All of that just sets us up so that
Dialogue: 0,0:02:13.62,0:02:15.60,Default,,0000,0000,0000,,we can use the Pythagorean Theorem.
Dialogue: 0,0:02:15.60,0:02:19.77,Default,,0000,0000,0000,,If we call this C, we know\Nthat A squared plus B squared
Dialogue: 0,0:02:21.94,0:02:25.29,Default,,0000,0000,0000,,is equal to C squared, or we\Ncould say that two squared ...
Dialogue: 0,0:02:25.29,0:02:26.83,Default,,0000,0000,0000,,Let me do it over here.
Dialogue: 0,0:02:26.83,0:02:28.100,Default,,0000,0000,0000,,Use that same red color.
Dialogue: 0,0:02:28.100,0:02:33.08,Default,,0000,0000,0000,,Two squared plus nine\Nsquared, plus nine squared,
Dialogue: 0,0:02:34.88,0:02:37.93,Default,,0000,0000,0000,,is going to be equal to\Nour hypotenuse square,
Dialogue: 0,0:02:37.93,0:02:40.49,Default,,0000,0000,0000,,which I'm just calling C, is\Ngoing to be equal to C squared,
Dialogue: 0,0:02:40.49,0:02:41.64,Default,,0000,0000,0000,,which is really the distance.
Dialogue: 0,0:02:41.64,0:02:43.40,Default,,0000,0000,0000,,That's what we're trying to figure out.
Dialogue: 0,0:02:43.40,0:02:47.57,Default,,0000,0000,0000,,Two squared, that is four,\Nplus nine squared is 81.
Dialogue: 0,0:02:50.17,0:02:53.90,Default,,0000,0000,0000,,That's going to be equal to C squared.
Dialogue: 0,0:02:53.90,0:02:56.57,Default,,0000,0000,0000,,We get C squared is equal to 85.
Dialogue: 0,0:02:57.43,0:02:59.85,Default,,0000,0000,0000,,C squared is equal to 85 or C
Dialogue: 0,0:03:00.74,0:03:04.42,Default,,0000,0000,0000,,is equal to the principal root of 85.
Dialogue: 0,0:03:04.42,0:03:06.92,Default,,0000,0000,0000,,Can I simplify that a little bit?
Dialogue: 0,0:03:06.92,0:03:07.93,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:03:07.93,0:03:11.06,Default,,0000,0000,0000,,How many times does five go into 85?
Dialogue: 0,0:03:11.06,0:03:14.15,Default,,0000,0000,0000,,It goes, let's see, it goes 17 times.
Dialogue: 0,0:03:16.09,0:03:17.86,Default,,0000,0000,0000,,Neither of those are perfect squares.
Dialogue: 0,0:03:17.86,0:03:19.100,Default,,0000,0000,0000,,Yeah, that's 50 plus 35.
Dialogue: 0,0:03:19.100,0:03:22.28,Default,,0000,0000,0000,,Yeah, I think that's about\Nas simple as I can write it.
Dialogue: 0,0:03:22.28,0:03:23.96,Default,,0000,0000,0000,,If you wanted to express it as a decimal,
Dialogue: 0,0:03:23.96,0:03:26.32,Default,,0000,0000,0000,,you could approximate it by\Nputting this into a calculator
Dialogue: 0,0:03:26.32,0:03:29.10,Default,,0000,0000,0000,,and however precise you want\Nyour approximation to be.
Dialogue: 0,0:03:29.10,0:03:31.81,Default,,0000,0000,0000,,That over here, that's\Nthe length of this line,
Dialogue: 0,0:03:31.81,0:03:33.36,Default,,0000,0000,0000,,our hypotenuse and our right triangle,
Dialogue: 0,0:03:33.36,0:03:35.06,Default,,0000,0000,0000,,but more importantly for\Nthe question they're asking,
Dialogue: 0,0:03:35.06,0:03:37.89,Default,,0000,0000,0000,,the distance between those points.