About this video
Sal performs a dilation on the coordinate plane centred at (9, -9) with scale factor 3. Each image point must be 3 times as far from the centre in both the x and y directions, so A(4, -3) maps to (-6, 9) and E maps to (-6, -3).
You'll be able to
- describe a dilation using its centre and scale factor.
- find the image of a point under a dilation by tripling its horizontal and vertical distances from the centre.
- check a dilation by comparing distances from the centre before and after.
Key words
- dilation
- A transformation that stretches or shrinks a figure from a fixed point by a scale factor.
- center of dilation
- The fixed point that the figure is stretched away from or shrunk towards.
- scale factor
- The number each distance from the centre is multiplied by in a dilation.
- image
- The new point or shape you get after a transformation.
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.
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