00:00Okay, next up is enlargements
00:03and again, this shouldn't take
00:05too long. So it says
00:06draw the enlargement of the
00:07triangle under the transformation matrix
00:092, 0, 0, 2. This
00:11is in the formula booklet.
00:12It was in the same
00:13place that all the transformations
00:14are. This time these two
00:16numbers are the same and
00:18these two are 0. You'll
00:21see again quite nicely easily
00:23why this ends up enlarging
00:27this shape.
00:28by scale vector of k
00:32or two in our situation.
00:34First though, before we even
00:34think about matrices, would we
00:37know how to enlarge this
00:40by scale vector two without
00:41the matrix? Well, I provided
00:43they give you the center
00:43zero zero. This is also
00:48for center zero zero. The
00:49center zero zero, you basically
00:51go out from this, so
00:53this is one one, then
00:55this point goes to two
00:56two. If this is three
00:59one, then this point goes
01:01to six two. So I'm
01:04going to go double each
01:05point six two, let's say
01:08is there. And then if
01:09this point is two two,
01:13the red point was two
01:14two will double that to
01:15four four. So this we're
01:17going to hear about here.
01:18So we'd look something like
01:21that. Anyway, even if you
01:23don't
01:24I'm going to start what
01:24I'm doing there. And more
01:26importantly, what I'm about to
01:27do now is how you
01:29do the transformation with the
01:31matrix. So you get your
01:33two, zero, zero, two, and
01:35then you get your points.
01:36Now you can do this,
01:37this works for one point
01:38or two points or three
01:40points in this case because
01:41it's a triangle I'm doing
01:42for three points. So I
01:43have my one, one, my
01:44two, two, and my three,
01:47one. And I just multiply
01:49these out. By the way
01:50guys, you've a calculator, you
01:51could do this with
01:52calculator. But I'm going to
01:54do it without a calculator
01:55to show you kind of
01:56why it works. So same
01:59thing. What it essentially does
02:01is doubles these coordinates because
02:04you do two times one
02:05plus zero times one, which
02:06is going to be two
02:07times two plus zero is
02:09four, two times three. So
02:10doubles these coordinates. And because
02:12I have the zero and
02:13the two here, it's just
02:14going to double the white
02:16coordinates as well. So I
02:17do zero times one, two
02:18times one is two, zero
02:20plus 4 and 2. So
02:24it just doubles both the
02:26x and the y -corner.
02:27Giving me the 2 -2,
02:29which is this guy, the
02:314 -4, which is this
02:32guy, and the 6 -2,
02:33which is this guy, which
02:35is essentially a triangle enlarged
02:41with the scale vector 2.
02:43Worth noting, guys, that the
02:46lengths of the triangle
02:48of the triangles are doubled,
02:51but the area of this
02:52triangle is actually four times
02:54the area of this triangle.
02:55It's too squared. I'll get
02:57to that a little bit
02:59more when we talk about
03:00the determinants, but you should
03:04know that anyway when you
03:05enlarge a shape, let me
03:06do a very quick example
03:08here. If you say this
03:10is a rectangle, say this
03:13side is two, and this
03:15side is three,
03:16You enlarge this rectangle by
03:19a scale vector of two.
03:21What you end up getting
03:22is now you double each
03:25side. So this side becomes
03:27four. This side becomes six.
03:29But if you do the
03:30area, the area of this
03:32is two times three, which
03:33is six. And the area
03:35of this one is six
03:36times four, which is 24.
03:39So the lengths are double,
03:41but the area is actually,
03:44times 4. It's 2 squared.
03:49Similarly, if you did, let
03:52me just do, imagine, I
03:58did an enlargement with the
04:00scale of like the 3.
04:01Now this guy is 6
04:03and this guy is 9
04:05because I'm not 2, 3.
04:06The area now is 54.
04:09It's actually 9 times bigger
04:11and it's 9 times bigger.
04:12the scale factor is 3,
04:15but the area factor is
04:179 because you square the
04:21scale factor. Anyway, the main
04:24thing I wanted to get
04:25from this video guys is
04:27the enlargement matrix is this
04:29form, the 2, 0, 0,
04:31and these two are the
04:31same number, and then you
04:33multiply the matrix by the
04:34points. It's important, guys, that
04:37you do the transformation matrix
04:39first,
04:40This times this, you don't
04:42do this times this even
04:45if it would work, it
04:46would give you a different
04:49answer. Okay, that's enlargements. I'll
04:52see you in the next
04:52video.