Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a shape but keeps its proportions the same. It can be an enlargement or a reduction.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much the shape will be enlarged or reduced. A scale factor greater than 1 enlarges the shape, 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 happens to the area of a shape when it is dilated by a scale factor of k?

Back

The area of the shape is multiplied by k².

Front

How do you determine the scale factor when given the original and dilated shapes?

Back

The scale factor can be determined by dividing the length of a side of the dilated shape by the length of the corresponding side of the original shape.

Front

What is the effect of a scale factor of 1 on a shape?

Back

A scale factor of 1 means the shape remains unchanged in size.

Front

If a triangle has vertices at (1, 2), (3, 4), and (5, 6), what are the coordinates after a dilation by a scale factor of 2?

Back

The new coordinates will be (2, 4), (6, 8), and (10, 12).

Front

What is the relationship between the original shape and the dilated shape?

Back

The original shape and the dilated shape are similar, meaning they have the same shape but different sizes.

Front

What is the formula for dilating a point A(x, y) by a scale factor of k?

Back

A' = (kx, ky).

Front

If a rectangle has a length of 4 and a width of 2, what will be its area after a dilation by a scale factor of 3?

Back

The area will be 36 (original area is 8, and after dilation, it is 8 * 3²).