Dilation Transformations in Geometry

This video tutorial covers the properties of dilations, a type of geometric transformation that changes the size of a figure while maintaining its shape. It explains the concept of scale factor, which determines whether a dilation is an enlargement or a reduction. The tutorial also discusses how to identify the center of dilation and calculate ratios using measurements and coordinates. Through examples, students learn to apply these concepts on a coordinate plane and understand the proportional relationships in dilations.

What is the primary difference between dilations and other transformations like translations, reflections, and rotations?

• Dilations change the shape of a figure.

• Dilations change the size of a figure.

• Dilations change the color of a figure.

• Dilations change the position of a figure.

What is the center of dilation?

• A point where all lines intersect.

• A point that remains fixed while the figure changes size.

• A point that moves with the figure.

• A point that changes color during dilation.

How do you determine the scale factor in a dilation?

• By subtracting the lengths of the image and pre-image.

• By adding the lengths of the image and pre-image.

• By multiplying the lengths of the image and pre-image.

• By dividing the length of the image by the length of the pre-image.

What remains unchanged in a dilation?

• The color of the figure.

• The size of the figure.

• The position of the figure.

• The shape of the figure.

When measuring segments in a dilation, what indicates that the distances are proportional?

• The ratios of the segments are equal.

• The segments are of different lengths.

• The segments are parallel.

• The segments are perpendicular.

How do you find the scale factor using coordinates on a coordinate plane?

• By multiplying the coordinates of the image and pre-image.

• By dividing the coordinates of the image by the coordinates of the pre-image.

• By adding the coordinates of the image and pre-image.

• By subtracting the coordinates of the image from the pre-image.

What does a scale factor greater than one indicate?

• An enlargement in size.

• No change in size.

• A reduction in size.

• A change in shape.

What does a scale factor less than one indicate?

• A reduction in size.

• An enlargement in size.

• No change in size.

• A change in shape.

If a triangle's image has sides twice as long as the pre-image, what is the scale factor?

• 0.5

• 2

• 1

• 3

What is the relationship between the angles of a figure and its dilated image?

• The angles are doubled.

• The angles change randomly.

• The angles are halved.

• The angles remain the same.