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### Course: Geometry (all content)>Unit 10

Lesson 6: Dilations

# Performing dilations

To dilate a point on a coordinate plane, you multiply its coordinates by a scale factor. The scale factor is a positive number that tells you how much to enlarge or shrink the point. If the scale factor is greater than 1, the point moves away from the origin. If the scale factor is less than 1, the point moves closer to the origin. Created by Sal Khan.

## Want to join the conversation?

• what would we do if the question doesn't have a point of dilation?
• 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.
• I feel like these comments are made by bots because this site is only used by 4th or lower grade levels but so many people are typing like middle school?
• Where did you get 18 from?
• 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)
• Has Sal ever gotten a question wrong?
• no he has never worked for a quest to help us out .
• I am having trouble as well and I have a test tomorrow.
• Do you know the equation for it though!
• How would I do this but with a fraction for the scale factor. Something like scale factor: 1/4
• it'd be (1/4x,1/4y) so you'd multiply the coordinates of each axis by 1/4 to get your dilation
(1 vote)
• Hi, everyone!
If the point of dilation is not given in the problem, which should I choose to center my dilation on: the origin, the center of the figure, a vertex of the figure, or some other point I'm not aware of?
Dilations have always confused me because of this very issue, but now that I'm studying for an exam I really need to understand it.
(1 vote)
• i can not figure out the answer
(1 vote)
• (a,b)=translation from center to origin d=dilation factor (x,y)= point being dilated

1) Translate center to origin (x+a, y+b)
2) Apply dilation (d(x+a), d(y+b))
3) Translate back (d(x+a)-a, d(y+b)-b)

(x,y) -> (d(x+a)-a, d(x+b)-b)
(1 vote)

## 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.