Drawing Images of Dilation with Negative Scale Factors

This lesson teaches how to draw images of dilation with negative scale factors using the center of dilation at the origin on the coordinate plane. It reviews basic dilation properties, such as parallel lines and collinearity, and provides examples with scale factors of -1, -2, and -1/2. Each example demonstrates how the image's orientation changes and how to calculate new vertex positions. The lesson concludes with a summary of the properties of dilations with negative scale factors.

What is a key property of a dilation when the segment does not pass through the center?

• It becomes perpendicular to the original segment.

• It remains on the same line as the original segment.

• It becomes a parallel line to the original segment.

• It disappears from the plane.

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

• They are divided by 2.

• They are doubled.

• They remain unchanged.

• They are multiplied by -1.

In a dilation with a scale factor of -2, how do you determine the position of the image vertices?

• By moving them twice the distance in the same direction.

• By moving them twice the distance in the opposite direction.

• By keeping them at the same distance.

• By moving them half the distance in the opposite direction.

What tool is suggested for measuring the lengths of segments in a dilation with a scale factor of -2?

• A protractor

• A ruler

• A calculator

• A compass

How does the size of the image compare to the preimage in a dilation with a scale factor of -1/2?

• The image is three times the size of the preimage.

• The image is the same size as the preimage.

• The image is half the size of the preimage.

• The image is twice as large as the preimage.

What is the orientation of the image in a dilation with a negative scale factor?

• It is in the opposite direction from the center.

• It mirrors the preimage.

• It rotates 90 degrees.

• It remains unchanged.

What is the relationship between the image size and the scale factor in dilations with negative scale factors?

• The image size is half the scale factor times the preimage size.

• The image size is the scale factor squared times the preimage size.

• The image size is the absolute value of the scale factor times the preimage size.

• The image size is the scale factor cubed times the preimage size.