Exploring Dilations in Geometry

What does a dilation in geometry refer to?

• Shifting an object from one position to another

• Rotating an object around a fixed point

• Enlarging or reducing an object while maintaining its proportions

• Changing the shape of an object

In the context of dilations, what does maintaining the same proportions mean?

• The object changes size but not shape

• The object changes position but not size

• The object changes color but not size

• The object changes both size and shape

How do you double the size of a triangle on a coordinate plane?

• By adding a fixed number to each coordinate

• By tripling each of the triangle's coordinates

• By doubling the distance between each point

• By doubling each of the triangle's coordinates

What is the scale factor in a dilation where the object's size is doubled?

• 4

• 0.5

• 2

• 1

If a triangle XYZ is dilated to triangle X'Y'Z', and triangle X'Y'Z' is larger, what is the dilation classified as?

• Enlargement

• Rotation

• Reduction

• Translation

How can you determine if a dilation is an enlargement or a reduction?

• By determining the color difference between the pre-image and the image

• By calculating the perimeter of the pre-image and the image

• By measuring the angles of the pre-image and the image

• By comparing the size of the pre-image and the image

What is the role of the scale factor in a dilation?

• It determines the angle of rotation

• It determines the direction of translation

• It determines the new size of the object

• It determines the color intensity of the object

What happens to the size of an object when the scale factor is less than 1?

• It becomes distorted

• It becomes smaller

• It becomes larger

• It remains the same

What does a scale factor of 1/2 indicate about a dilation?

• The object's size is reduced by half

• The object's size increases fourfold

• The object's size remains unchanged

• The object's size doubles

If you wanted to make a geometric figure three times as large, what would the scale factor be?

• 1/3

• 0.5

• 3

• 1