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## Congruence and similarity

Current time:0:00Total duration:2:26

# Dilating shapes: shrinking by 1/2

CCSS Math: HSG.SRT.A.1, HSG.SRT.A.1b, HSG.SRT.A.2

## Video transcript

Plot the images of points
D, E, and F after a dilation centered at 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 D, E, and F are going to be half as far away from
the origin, because our scale factor is 1/2 in
either direction. So for example, let's
think about point D first. Point D is at negative 8. So 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 4.5. 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 1
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 1/2 is 3 and 1/2. So we're going to stick
it right over there. And then finally F, its
x-coordinate is 6 more than the origin. Its y-coordinate is 6 less. So its image after
scaling is going to be 3 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 points. So if you were to
connect these points, you would essentially
have dilated down DEF, and your center of dilation
would be the origin. So let's just write
these coordinates. Point D-- and point D, remember,
was the point negative 8, negative 9. That's going to map to--
take 1/2 of each of those. So negative 4 and negative 4.5. Point E maps to--
well, E was at 2, 7. So it maps to 1, 3.5. And then finally, point
F was at 6, negative 6, so 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.