Dilation and Triangle Properties

The video tutorial explains the process of graphing a pre-image and its dilation with a scale factor between zero and one, resulting in a reduction. It covers the calculation of vertices and graphing the image. The tutorial then explores the concept of similarity by comparing the ratio of perimeters to the scale factor. It involves calculating the perimeter of a right triangle using the Pythagorean theorem. Finally, the video discusses the ratio of areas between the image and pre-image, highlighting its relation to the square of the perimeter ratio.

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

• Comparing the perimeters of the triangles

• Finding the hypotenuse of the triangle

• Graphing the pre-image of the triangle

• Calculating the area of the triangle

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

• A reflection

• An enlargement

• No change

• A reduction

How are the vertices of the image calculated after dilation?

• By dividing each coordinate by the scale factor

• By subtracting the scale factor from each coordinate

• By multiplying each coordinate by the scale factor

• By adding the scale factor to each coordinate

What is the perimeter of the pre-image triangle?

• 36

• 24

• 48

• 30

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

• 3 to 2

• 4 to 5

• 2 to 3

• 1 to 1

How is the hypotenuse of the image triangle calculated?

• By multiplying the base and height

• By subtracting the base from the height

• By adding the base and height

• By using the Pythagorean theorem

What is the area of the pre-image triangle?

• 24

• 36

• 54

• 18

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

• 4 to 9

• 2 to 3

• 3 to 4

• 1 to 2

How is the area of a right triangle calculated?

• Base minus height

• Base times height

• Base plus height

• Half of base times height

What is the relationship between the area ratio and the scale factor?

• The area ratio is the same as the scale factor

• The area ratio is double the scale factor

• The area ratio is half of the scale factor

• The area ratio is the square of the scale factor