Dilation and Scale Factors in Geometry

This video tutorial explains how to draw images of dilation using different scale factors and centers of dilation. It covers four examples: dilation with a scale factor of 2 centered at the origin, dilation with a scale factor of 0.5 centered inside the pre-image, dilation with a scale factor of 2 centered on the pre-image, and dilation with a scale factor of 3 centered outside the pre-image. The tutorial emphasizes the importance of understanding the center of dilation and its role in the dilation process.

What is the result of applying a scale factor of 2 to a pre-image?

• The image is half the size of the pre-image.

• The image is twice the size of the pre-image.

• The image is four times the size of the pre-image.

• The image remains the same size.

When the center of dilation is inside the pre-image, what is the first step in drawing the image?

• Calculate the area of the pre-image.

• Rotate the pre-image around the center.

• Draw rays from the center through each vertex.

• Multiply the coordinates by the scale factor.

If the scale factor is 1/2, how do you determine the position of the image's vertices?

• Keep the vertices at the same distance from the center.

• Halve the distance from the center to each vertex.

• Double the distance from the center to each vertex.

• Triple the distance from the center to each vertex.

What happens to the image when the center of dilation is on the pre-image?

• The image is not affected by the center's position.

• The image is rotated around the center.

• The image is reflected across the center.

• The image lies on the same line as the pre-image.

How do you calculate the new position of a vertex when the center is on the pre-image and the scale factor is 2?

• Add the original distance to the center.

• Subtract the original distance from the center.

• Divide the original distance by 2.

• Multiply the original distance by 2.

What is the method used to find the image when the center of dilation is outside the pre-image?

• Rotate the pre-image around the center.

• Reflect the pre-image across the center.

• Translate the pre-image away from the center.

• Multiply the coordinates by the scale factor.

In a dilation with a scale factor of 3, what happens to the coordinates of the pre-image?

• They are divided by 3.

• They are added to the center's coordinates.

• They remain unchanged.

• They are multiplied by 3.

Where can the center of dilation be located in relation to the pre-image?

• Only outside the pre-image.

• Only inside the pre-image.

• Inside, on, or outside the pre-image.

• Only on the pre-image.

Which example demonstrates the center of dilation being inside the pre-image?

• None of the examples.

• The example with a scale factor of 1/2.

• The example with a scale factor of 2.

• The example with a scale factor of 3.

What is a common misunderstanding about the center of dilation?

• It is the point from which the dilation occurs.

• It is always at the center of the pre-image.

• It can only be outside the pre-image.

• It must be on the pre-image.