Identifying center of dilation with no grid

0:00- [Instructor] We are told triangle STR is the image of triangle SMH after a dilation. So STR is this big triangle here. SMH is the smaller one. Which point is the center of dilation for this transformation? Pause this video, have a go at that. Okay, so the important thing to realize is, let's say I have some point, let's say that this is the true center of dilation.

0:24I just won't write C just that might confuse us with that point. Any other point before dilation, if I were to dilate it, if I were to scale this by a factor of let's say two, whatever this distance is, is going to go twice as far. So if this distance is, let's call this x, then I'd go in the same direction.

0:45I'd go in the same direction, but twice as far. So after the dilation, I would move over here. So the only way that if a point does not shift after a dilation is if it is the actual center of dilation. Because if there's a point right at the center of dilation, it's zero away from the center.

1:09So if you go two times away from that or 100 times 0, you're still right over there. And we can see in this example right over here, even after the dilation, this point S does not change; it stays where it is, so that is the center of the dilation for this transformation.

1:31If you thought it was point C, because that kind of looks like something interesting and it even has the C there, maybe you think C for center, well then the new S, the thing, the image after it's dilated would've gotten further away, but that's not what happened here; it just stayed in place.