Dilating points

- [Instructor] We're asked to plot the image of point A under a dilation about point P with a scale factor of three. So what they're saying when they say under a dilation, they're saying stretching it or scaling it up or down around the point P. Now so what we're going to do is just think about, well how far is point A and then we want to dilate it with a scale factor of three. So however far A is from point P, it's going to be three times further under the dilation. Three times further in the same direction. So how do we think about that? Well, one way to think about it is to go from P to A you have to go one down and two to the left, so minus one and minus two. And so if you dilate it with a factor of three, then you're going to want to go three times as far down. So minus three, and three times as far to the left, so you'll go minus six. So one, let me do this, so negative one, negative two, negative three, negative four, negative five, negative six. So you will end up right over there. And you can even see it, that this is indeed three times as far from P in the same direction. So we could call the image of point A, maybe we call that A prime, and so there you have it. It has been dilated with a scale factor of three. And so you might be saying, wait, I'm used to dilating being stretching or scaling. How have I stretched or scaled something? Well imagine a bunch of points here that represents some type of picture and if you push them all three times further from point P, which you could do as your center of dilation, then you would expand the size of your picture by a scale factor of three. Let's do another example with a point. So, here we're told, plot the image of point A under a dilation about the origin with a scale factor of 1/3 so first of all we don't even see the point A here, so it's actually below the fold. So let's see, there we go, that's our point A. We want it to be about the origin, so about the point zero zero. This is what we want to, the dilation about the origin with a scale factor of 1/3, scale is 1/3. Scale factor, I should say. So how do we do this? Well here, however far A is from the origin we now want to be in the same direction, but 1/3 as far. So one way to think about it, to go from the origin to A you have to go six down and three to the right. So 1/3 of that would be two down and one to the right. Two is 1/3 of six and one is 1/3 of three, so you will end up right over here. That would be our A prime. So notice, you are 1/3 away from the origin as we were before because once again, this is point A under a dilation about the origin with a scale factor of 1/3.