Dilation with Negative Scale Factors

This video tutorial explains how to perform dilations with negative scale factors, using the center of dilation at the origin on a coordinate plane. It reviews basic dilation properties and provides three examples with different negative scale factors: -1, -2, and -1/2. Each example demonstrates how the image is oriented in the opposite direction from the pre-image and how the size of the image relates to the absolute value of the scale factor. The tutorial concludes with a summary of the key properties of dilations with negative scale factors.

What happens to a segment that does not pass through the center during a dilation?

• It becomes perpendicular to the original segment.

• It becomes parallel to the original segment.

• It disappears.

• It remains unchanged.

In a dilation with a negative scale factor, what is the relationship between the pre-image and image vertices?

• They are identical.

• They are parallel to each other.

• They are collinear with the center.

• They are always perpendicular.

When performing a dilation with a scale factor of -1, what happens to the coordinates of the vertices?

• They are halved.

• They are doubled.

• They remain the same.

• They are negated.

In the example with a scale factor of -2, what is the first step to find the image location?

• Draw lines from the center through each vertex.

• Translate the image by 2 units.

• Multiply the coordinates by -2.

• Rotate the image 180 degrees.

How do you determine the new position of a vertex in a dilation with a scale factor of -2?

• Move it half the distance in the opposite direction.

• Move it half the distance in the same direction.

• Move it twice the distance in the opposite direction.

• Move it twice the distance in the same direction.

What is the effect of a scale factor of -1/2 on the size of the image compared to the pre-image?

• The image is three times as large.

• The image is the same size.

• The image is half the size.

• The image is twice as large.

In a dilation with a negative scale factor, how does the orientation of the image compare to the pre-image?

• The orientation remains the same.

• The orientation is reversed.

• The orientation is rotated 90 degrees.

• The orientation is unchanged.

What is a key property of dilations with negative scale factors regarding the image size?

• The image size is always larger than the pre-image.

• The image size is equal to the absolute value of the scale factor times the pre-image size.

• The image size is always smaller than the pre-image.

• The image size is unpredictable.

What is the effect of a negative scale factor on the direction of the image?

• The image moves in the same direction as the pre-image.

• The image moves randomly.

• The image remains stationary.

• The image moves in the opposite direction from the center.

Which of the following is true for all dilations with negative scale factors?

• The image is always smaller than the pre-image.

• The image is always larger than the pre-image.

• The image is always in the opposite direction from the center.

• The image is always identical to the pre-image.