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## Geometry (all content)

# Performing dilations

CCSS.Math: ,

Sal shows how to perform a dilation on a hexagon using our interactive widget! Created by Sal Khan.

## Want to join the conversation?

- what would we do if the question doesn't have a point of dilation?(1 vote)
- Well, depends on what the question's asking for, but generally I'd say probably pick 0,0 or some other arbitrary point - 0,0 is easiest, and if it didn't give you the point of dilation it must not be important to the answer.(15 votes)

- Where did you get 18 from?(4 votes)
- Sal multiplied the vertical distance between A and the point of dilation by 3 in order to obtain the y coordinate of A'(1 vote)

- How would I do this but with a fraction for the scale factor. Something like scale factor: 1/4(4 votes)
- I think you multiply it by the coordinates? I don't know I didn't really understand it(1 vote)

- where did the fifteen come from(4 votes)
- Sal multiplied the horizontal distance between A and the point of dilation by 3 in order to obtain the x coordinate of A'(0 votes)

- A dilation causes figures to become not congruent, but they remain similar right?(2 votes)
- Correct, the figures remain similar because nothing changes but the size.(2 votes)

- I HATE THIS CLASS HELP ME! the mans voice sounds so amazing it deserves to be in a ASMR video(0 votes)
- Pay attention, it may help you with a quiz. It'll help you learn. It's important to pay ateention, even though it may seem boring.(6 votes)

- what do i do if its a word problem without a graph(2 votes)
- When you dilate an object and you have a point of dilation, does that matter when you calculate the new points such as A' or B'? Do you multiply (9,-9) by anything?(2 votes)
- I am having trouble as well and I have a test tomorrow.(3 votes)
- Thanks Sal! I just have one question: some of us don't have the fancy dilation tools and what not. My math homework, that I desperately need help on is on a paper no online. What do I do then?(2 votes)

## Video transcript

Perform a dilation on
the coordinate plane. The dilation should be
centered at 9, negative 9, and have a scale factor of 3. So we get our dilation tool out. We'll center it-- actually, so
it's already actually centered at 9, negative 9. We could put this
wherever we want, but let's center it
at 9, negative 9. And we want to
scale this up by 3. So one way to think about it
is, pick any of these points right over here, and they're
going to have to get 3 times further away from our
center of dilation. So for example, this
point C-- actually let's think about these
points where they actually want us to fill something in. So point A right over here, it
is at the point 4, negative 3. So in the x direction,
it is 5 less than 9. We want it to be 3
times further than 9. So we want it to
be 15 less than 9. So we want the x-coordinate of
A, 9 minus 15 is negative 6. We want it to go to negative 6. And likewise, we want its
y-coordinate to be 3 times further. So right now, let's
see, it is at negative 3 relative to negative 9, so it
is 6 more on the y direction. We want it to be 18 more. 18 more than negative
9 would be positive 9. So point A should map
to negative 6 comma 9. And that should give
us enough information to just make sure that we are
dilating up by a factor of 3. So let's see. Let's dilate up
by a factor of 3. So we want to get the image of
point A to the point negative 6 comma 9. So we are there. There we go. We have dilated it up. And then we could
even look where the point that corresponds
to E has mapped to. And you can look at each
direction, it's 3 times further. E is now at negative
6 comma negative 3. The images of point A
and E are 3 times as far as the original points. 3 times far apart, I should
say, as the original points. And they're 3 times further
from our center of dilation right over here. You see, for example, point
E has the x-coordinate of 4, which is 5 less. Now it is at
negative 6, which is 15 less than our
center of dilation. And the same thing true,
its y-coordinate is 2 more. And now after we mapped
it, its y-coordinate is 6 more than our
center of dilation. Got it right.