Geometric Transformations and Ratios

The video tutorial explains how to graph a pre-image and perform a dilation with a scale factor between zero and one, resulting in a reduction. It covers calculating the vertices, graphing the image, and understanding the relationship between the pre-image and image. The tutorial also explores the ratio of perimeters and areas, comparing them to the scale factor, and demonstrates the use of the Pythagorean theorem to find triangle sides. The final section highlights the relationship between the area ratio and the square of the perimeter ratio.

What is the effect of a scale factor between zero and one on a geometric figure?

• It enlarges the figure.

• It reduces the figure.

• It keeps the figure the same size.

• It flips the figure.

When dilating a figure around the origin, what operation is performed on the coordinates?

• Add the scale factor to each coordinate.

• Subtract the scale factor from each coordinate.

• Divide each coordinate by the scale factor.

• Multiply each coordinate by the scale factor.

What is the relationship between the pre-image and image in terms of similarity?

• They have the same area.

• They have the same perimeter.

• They are always congruent.

• They have proportional sides.

How can you find the third side of a right triangle if you know the other two sides?

• Multiply the two sides together.

• Subtract the smaller side from the larger side.

• Add the two sides together.

• Use the Pythagorean theorem.

What is the perimeter of the image if the sides are 6, 8, and 10?

• 18

• 30

• 24

• 36

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

• 1:1

• 2:3

• 4:5

• 3:4

How is the area of a right triangle calculated?

• Base times height

• Half the product of the base and height

• Sum of the base and height

• Difference between the base and height

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

• 4:9

• 5:6

• 2:3

• 3:4

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

• It is the same as the scale factor.

• It is the square of the scale factor.

• It is the cube of the scale factor.

• It is unrelated to the scale factor.

What is the significance of the ratio of the perimeters in relation to the scale factor?

• It is equal to the scale factor.

• It is unrelated to the scale factor.

• It is the square of the scale factor.

• It is the inverse of the scale factor.