Dilating points

we're asked to plot the image of point a under a dilation about point P with a scale factor of 3 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 and that's 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 3 so however far a is from point P it's going to be 3 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 1 and minus 2 and so if you dilate it with the factor of 3 then you're gonna want to go 3 times as far down so minus 3 minus 3 and 3 times as far to the left so you'll go minus 6 so 1 or that's let me do this so negative 1 negative 2 negative 3 negative 4 negative 5 negative 6 so you will end up right over there and you can even see it that this is indeed 3 times as far from P in the same direction and 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 3 and so you might be saying wait I'm used to dilation being stretching or scaling how if I stretched or scaled something well imagine a bunch of points here that represents some type of picture and if you push them all 3 times further from point P which you could use your center of dilation then you would expand the size of your picture by a scale factor of 3 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 with a scale factor of 1/3 scale is one-third 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 one third 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 one third of that would be two down and one to the right - or two is one third of six and one is one third of three so you will end up right over here that would be our a prime and so notice you are one third as far 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