Dilations!

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a center point and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you find the image of a point under dilation?

Back

To find the image of a point under dilation, multiply the coordinates of the original point by the scale factor.

Front

What is the image of the point (4, 6) under a dilation with a scale factor of 3?

Back

The image is (12, 18) because (4*3, 6*3) = (12, 18).

Front

If the point (2, 3) is dilated by a scale factor of 1/2, what is the new coordinate?

Back

The new coordinate is (1, 1.5) because (2*1/2, 3*1/2) = (1, 1.5).

Front

What happens to a figure when it is dilated by a scale factor of 1?

Back

When a figure is dilated by a scale factor of 1, it remains unchanged in size and shape.

Front

What is the difference between enlargement and reduction in dilation?

Back

Enlargement occurs when the scale factor is greater than 1, while reduction occurs when the scale factor is between 0 and 1.

Front

If a polygon is dilated by a scale factor of 2, what can be said about the original and the image?

Back

The image will be twice the size of the original polygon, but they will not be congruent.

Front

What is the scale factor if the point (10, 15) is dilated to (5, 7.5)?

Back

The scale factor is 1/2, calculated by dividing the coordinates of the image by the coordinates of the original point.

Front

True or False: A dilation with a scale factor of 1/4 results in an enlargement.

Back

False. A scale factor of 1/4 results in a reduction.