Exploring Dilations and Their Impact on Perimeter and Area

What does a dilation in geometry refer to?

• A transformation that rotates a figure around a point

• A transformation that changes the size of a figure while maintaining its shape

• A transformation that slides a figure on the coordinate plane

• A transformation that changes the shape of a figure

How do you label the image vertices after dilation?

• Using the same letters as the pre-image

• Using numerical indices

• Adding a prime symbol to the pre-image vertices

• Using different letters in alphabetical order

What does the prime symbol (') indicate in geometry?

• The midpoint of a line segment

• The figure after transformation

• The original figure before transformation

• The intersection point of two lines

What indicates a dilation resulted in an enlargement?

• The scale factor is greater than 1

• The scale factor is 0

• The scale factor is equal to 1

• The scale factor is less than 1

How is the new perimeter of a dilated figure calculated?

• By multiplying the original perimeter by the scale factor

• By adding the scale factor to the original perimeter

• By subtracting the scale factor from the original perimeter

• By dividing the original perimeter by the scale factor

How do you determine if a dilation is a reduction?

• When the scale factor is 0

• When the scale factor is less than 1

• When the scale factor is equal to 1

• When the scale factor is greater than 1

What is the correct formula to find the area of a dilated figure?

• Original area multiplied by the square of the scale factor

• Original area plus the scale factor

• Original area divided by the scale factor

• Original area multiplied by the scale factor

In the practical example, what was the scale factor for the field compared to the playground?

• 4.0

• 3.2

• 2.4

• 1.6

What is the effect of dilation on the perimeter and area of a figure?

• Both perimeter and area remain unchanged

• Perimeter is multiplied by the scale factor, area by the square of the scale factor

• Perimeter is multiplied by the square of the scale factor, area by the scale factor

• Both perimeter and area are multiplied by the scale factor

Which statement is true regarding the area of the field and playground?

• The area of the field is half the area of the playground

• The area of the field is 10.24 times the area of the playground

• The area of the field is equal to the area of the playground

• The area of the field is 6.4 times the area of the playground