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 scale factor.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates the ratio of the length of a side of the new figure to the length of the corresponding side of the original figure.

Front

How do you write the algebraic notation for a dilation with a scale factor of 2?

Back

(x, y) goes to (2x, 2y).

Front

What happens to a point (x, y) when it is dilated by a scale factor of 1/2?

Back

(x, y) goes to (1/2x, 1/2y).

Front

If a figure is dilated by a scale factor greater than 1, what type of transformation occurs?

Back

An enlargement occurs.

Front

If a figure is dilated by a scale factor less than 1, what type of transformation occurs?

Back

A reduction occurs.

Front

What is the center of dilation?

Back

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

Front

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

Back

Multiply the coordinates of the point by the scale factor.

Front

What is the effect of a scale factor of -1 on a point (x, y)?

Back

The point is reflected across the origin, resulting in (-x, -y).

Front

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

Back

The dilated figure is similar to the original figure, meaning they have the same shape but different sizes.