CP 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. It is defined by a center point and a scale factor.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 indicates enlargement, while a scale factor between 0 and 1 indicates reduction.

Front

If a triangle has a side length of 5 units and is dilated with a scale factor of 3, what is the new side length?

Back

15 units.

Front

What happens to the coordinates of a point (x, y) when it undergoes a dilation about the origin with a scale factor k?

Back

The new coordinates will be (kx, ky).

Front

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

Back

If the scale factor is greater than 1, it is an enlargement. If the scale factor is between 0 and 1, it is a reduction.

Front

What is the effect of a dilation on angles in a figure?

Back

Dilation does not change the measures of angles; it preserves angle measures.

Front

If a rectangle is 2 inches by 4 inches and is dilated by a scale factor of 2, what are the new dimensions?

Back

4 inches by 8 inches.

Front

What is the relationship between the original area and the area after dilation?

Back

The area of a figure after dilation is multiplied by the square of the scale factor. If the scale factor is k, the new area is k^2 times the original area.

Front

If a triangle has an area of 10 square units and is dilated by a scale factor of 2, what is the new area?

Back

40 square units.

Front

What is the formula for calculating the new length after dilation?

Back

New Length = Original Length × Scale Factor.