Understanding Dilation and Scale Factors

The video tutorial covers the concept of dilations, a type of transformation that changes the size of an image through enlargement or reduction. It explains how to determine the scale factor, which is the ratio of the lengths of corresponding sides of similar polygons. The tutorial includes examples using triangles and index cards to illustrate how to calculate the scale factor and identify whether a transformation is an enlargement or reduction. It also demonstrates how to use coordinates to find the scale factor when side lengths are not provided.

What is a dilation in geometry?

• A transformation that rotates an image.

• A transformation that results in the enlargement or reduction of an image.

• A transformation that results in an image being congruent to the original.

• A transformation that changes the shape of an image.

Which of the following is true about a scale factor greater than 1?

• It results in a reduction.

• It results in a rotation.

• It results in an enlargement.

• It results in a congruent shape.

How do you calculate the scale factor in a dilation?

• Sum of old and new lengths.

• Old length divided by new length.

• New length divided by old length.

• Difference between old and new lengths.

In the triangle example, what was the scale factor found?

• 3

• 4

• 2

• 1

What does a scale factor of 2 indicate about the dilation?

• The image is rotated.

• The image remains the same size.

• The image is enlarged by twice the size.

• The image is reduced by half.

In the index card example, what was the scale factor calculated?

• 3

• 2

• 4

• 1

What does a scale factor of 3 indicate in the index card example?

• The large card is half the size of the small card.

• The large card is the same size as the small card.

• The large card is one-third the size of the small card.

• The large card is three times the size of the small card.

How can you find the scale factor if side lengths are not given?

• By using the area of the shapes.

• By using the perimeter of the shapes.

• By using the volume of the shapes.

• By using the coordinates of the points.

What is the scale factor if the coordinates of a point change from (4, 4) to (3, 3)?

• 1.25

• 1

• 0.5

• 0.75

If a point's coordinates change from (-4, 2) to (-3, 1.5), what is the scale factor?

• 0.5

• 1.5

• 0.75

• 1