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# Dilating shapes: shrinking by 1/2

CCSS.Math:

## Video transcript

plot the images of points de and F after dilation centered the origin with a scale factor of 1/2 so we're going to center around the origin we want to scale this thing down by 1/2 so one way to think about it is the points that will correspond to points de and F are going to be 1/2 as far away from the origin because of our scale factor is 1/2 in either direction so for example let's let's think about Point D first Point D is at negative 8 so if we scale if we have a scale factor of 1/2 what point D will map to is going to be at negative 4 on the x-direction and on the y-direction D is at negative 9 so this is going to be at negative 4 point 5 half of that so that is going to be right over there that's where point D is going to be or the image of point D after the scaling now let's think about point E e is 2 more than the origin in the X direction so it's only going to be one more once we scale it by 1/2 and it's 7 more in the Y direction so it's going to be at 3 and 1/2 7 times one half is three and 1/2 so we're going to stick it right over there and then finally F it's 6 its x-coordinate is 6 more than the origin and its y-coordinate is 6 less so it's image after scaling is going to be three more in the x-direction and 3 less in the y-direction so it's going to be right over there so we've plotted the images of the point so if you were to connect these points you would essentially have dilated down d EF with the center at with width and your center of dilation would be the origin so let's just write these coordinates point D and point D remember what's the point negative 8 negative 9 that's going to map to well we're going to take half of each of those so negative 4 and negative 4 point 5 point e maps to well II was it's at 2 7 so it maps to 1 3.5 3.5 and then finally Point F was it 6 negative 6 so it maps to 3 it maps to 3 negative 3 so the important thing to recognize is the center of our dilation was the origin so in each dimension in the X direction or in the Y direction we just halved the distance from the origin because the scale factor was 1/2 we got it right