Dilations Quick Check

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape, using a scale factor and a center of dilation.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates how much larger or smaller a figure will be after the dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a point (x, y) is dilated by a scale factor of k, what are the new coordinates?

Back

The new coordinates will be (kx, ky).

Front

What is the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted during the dilation.

Front

True or False: A dilation produces a similar figure. Why?

Back

True. A dilation produces a similar figure because it maintains the shape but changes the size.

Front

What happens to the angles of a figure during a dilation?

Back

The angles of a figure remain unchanged during a dilation.

Front

If a figure is dilated by a scale factor of 2, what happens to its area?

Back

The area of the figure is multiplied by the square of the scale factor. So, if the scale factor is 2, the area is multiplied by 2² = 4.

Front

What is the difference between congruent figures and similar figures?

Back

Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size.

Front

If a potion bottle is enlarged by a scale factor of 3, what is the new volume if the original volume is V?

Back

The new volume will be 3³ * V = 27V.

Front

What is the effect of the Engorgio charm in Harry Potter?

Back

The Engorgio charm enlarges an object, effectively applying a dilation with a scale factor greater than 1.