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 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.

Front

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

Back

A' = (kx, ky)

Front

What happens to the coordinates of a point when it is dilated by a scale factor greater than 1?

Back

The coordinates of the point increase, making the figure larger.

Front

What happens to the coordinates of a point when it is dilated by a scale factor between 0 and 1?

Back

The coordinates of the point decrease, making the figure smaller.

Front

How do you find the image of a point under dilation with the origin as the center?

Back

Multiply each coordinate of the point by the scale factor.

Front

What are the coordinates of the image of point B(4, 9) under a dilation with a scale factor of 2?

Back

B' (8, 18)

Front

If triangle ABC is dilated to triangle DEF with a scale factor of 2, what is the relationship between the lengths of corresponding sides?

Back

The lengths of the sides of triangle DEF are twice the lengths of the corresponding sides of triangle ABC.

Front

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

Back

Dilation does not change the measures of angles; they remain the same.

Front

If a figure is dilated by a scale factor of 3, what is the new area compared to the original area?

Back

The new area is 9 times the original area, since area scales by the square of the scale factor.