Dilation and Triangle Properties

The video tutorial explains the process of graphing a pre-image and performing a dilation with a scale factor between zero and one, resulting in a reduction. It covers calculating the perimeter of both the pre-image and image, comparing their ratios, and understanding how these relate to the scale factor. The tutorial also explores the relationship between the areas of the image and pre-image, showing that the area ratio is the square of the perimeter ratio.

What is the first step in solving the multi-step problem presented in the video?

• Finding the hypotenuse of the triangle

• Graphing the pre-image of the triangle

• Calculating the area of the triangle

• Comparing the perimeters of the triangles

What does a scale factor between zero and one indicate in terms of dilation?

• An enlargement

• A reduction

• A reflection

• No change

When dilating around the origin, how are the new vertices calculated?

• By adding the scale factor to each coordinate

• By subtracting the scale factor from each coordinate

• By multiplying each coordinate by the scale factor

• By dividing each coordinate by the scale factor

What is compared to the scale factor in the video?

• The ratio of the perimeters

• The ratio of the areas

• The coordinates of the vertices

• The length of the hypotenuse

How is the perimeter of the pre-image calculated?

• By multiplying the base and height

• By adding the lengths of all sides

• By using the Pythagorean theorem

• By subtracting the coordinates

What is the ratio of the perimeter of the image to the pre-image?

• 4 to 5

• 1 to 1

• 2 to 3

• 3 to 2

Which two measurements are used to calculate the area of a right triangle?

• Base and hypotenuse

• Height and hypotenuse

• All three sides

• Base and height

How is the ratio of the areas related to the scale factor?

• It is the square of the scale factor

• It is unrelated to the scale factor

• It is the same as the scale factor

• It is the cube of the scale factor