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Current time:0:00Total duration:2:43

Video transcript

we are told the triangle n prime is the image of triangle n under a dilation so this is n prime and in this red color and then n is the original and is in this blue color what is the center of dilation and they give us some choices here choice a B C or D as a center of dilation so pause this video and see if you can figure it out on your own so there's a couple of ways to think about it one way I like to just first think about what is the what is the scale factor here so in our original n we have this side here it has a length of 2 and then once we dilated it by and use that scale factor that corresponding side has a length of 4 so we went from 2 to 4 so we can figure out our scale factor scale factor is equal to 2 2 times 2 is equal to 4 now what about our center of dilation so one way to think about it is pick two corresponding points so let's say we were to pick this point and this point so the image the corresponding point on n prime is going to be the scale factor as far away from our center of dilation as the original point so in this example we know the scale factor is 2 so this is going to be twice as far from our center of dilation as the corresponding point well you can immediately see and it's going to be in the same direction so actually a little bit if you just draw a line connecting these two there's actually only one choice that sits on that line and that is choice D right over here as being the center of dilation and you can also verify that notice this first point on the original triangle it's change in X is 2 and it's change in Y is 3 to 3 to go from point D to point to that point and then if you want to go to point D to its image well now you got to go twice as far your change in X is 4 and your change in Y is 6 you could use the Pythagorean theorem to calculate this distance and then the longer distance but what you see is is that the corresponding point is now twice as far from your center of dilation so there's a couple of ways to think about it one if you connect corresponding points your center of dilation is going to be on a line that connects those two points and that the image should be the scale factor as far away from the center of dilation in this case it should be twice as far from the center of dilation as the point that it is the image of