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Holt Mathematics Course 3 Chapter 5 Lesson 6

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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.

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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.

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Sal is given a rectangle on the coordinate plane and he draws the image of the rectangle under a dilation with scale factor 1 2/3 about an arbitrary point.

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How Do You Make a Figure Larger Using a Dilation? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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Sal dilates a shape and then compares the side lengths of the pre-image and image.

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Sal shows how to perform a dilation on a hexagon using our interactive widget!

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When someone's eyes dilate, their pupils get bigger or smaller, but they always stay the same shape. Dilation in math is very similar. When you dilate a figure, you change the size of the figure without changing its shape. This tutorial introduces you to dilation. Take a look!

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.