This video tutorial covers the concept of dilations in geometry, including how to draw and analyze dilated images, calculate scale factors, and perform dilations on the coordinate plane. It explains the ratio method for drawing dilated images and discusses the importance of congruent angles and proportional side lengths in determining similarity. The tutorial also covers how to find scale factors and differentiate between enlargement and reduction, as well as how to perform dilations centered at the origin and other points.

What is a dilation in geometry?

• A transformation that changes the shape of a figure.

• A transformation that changes the size but not the shape of a figure.

• A transformation that rotates a figure.

• A transformation that translates a figure.

What does the term 'dilate' mean in the context of geometry?

• To change the color of a figure.

• To change the orientation of a figure.

• To reflect a figure across an axis.

• To enlarge or reduce a figure while maintaining its shape.

What is the first step in the ratio method for drawing a dilated image?

• Connect the vertices of the figure.

• Measure the distance from the center of dilation to a vertex.

• Draw a new figure with random measurements.

• Calculate the area of the original figure.

In the ratio method, what is done after measuring the distance from the center of dilation?

• Add the scale factor to the distance.

• Multiply the distance by the scale factor.

• Subtract the scale factor from the distance.

• Divide the distance by the scale factor.

What is the final step in the ratio method for drawing a dilated image?

• Calculate the perimeter of the new figure.

• Connect the new points to form the dilated image.

• Color the new figure.

• Erase the original figure.

How can you determine if two figures are similar after a dilation?

• By checking if they have the same number of sides.

• By comparing their perimeters.

• By ensuring all angles are congruent and side lengths are proportional.

• By checking if their areas are equal.

What does a prime symbol (') indicate in a dilated figure?

• The figure is original.

• The figure has been rotated.

• The figure has been translated.

• The figure has been modified or moved.

What is a scale factor in the context of dilations?

• The number of sides in a figure.

• The ratio of side lengths in the image to the preimage.

• The angle of rotation for a figure.

• The distance between two points in a figure.

If a figure is enlarged, what can be said about its scale factor?

• It is greater than 1.

• It is equal to 1.

• It is less than 1.

• It is negative.

What happens to a figure when the scale factor is less than 1?

• The figure is enlarged.

• The figure is reduced.

• The figure is rotated.

• The figure is translated.