Understanding Dilations in Geometry

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 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

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

Back

Multiply the coordinates of the point by the scale factor.

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor k?

Back

The new coordinates become (kx, ky).

Front

If a point (4, 6) is dilated by a scale factor of 3, what are the new coordinates?

Back

(12, 18).

Front

What is the effect of a scale factor less than 1 on a figure?

Back

It reduces the size of the figure.

Front

What is the effect of a scale factor greater than 1 on a figure?

Back

It enlarges the size of the figure.

Front

If the center of dilation is at the origin, how do you calculate the image of point B (-10, -6) with scale factor k = 1/2?

Back

Multiply each coordinate by 1/2: (-10 * 1/2, -6 * 1/2) = (-5, -3).

Front

What mathematical operation is used with the scale factor in a dilation?

Back

Multiplication.

Front

If a point (8, 12) is dilated to (2, 3), what is the scale factor?

Back

1/4.