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

What type of motion is a dilation?

Back

Dilation is classified as 'Not Rigid Motion' because it changes the size of the figure.

Front

How is the scale factor applied in a dilation?

Back

The scale factor is applied by multiplying the coordinates of each point in the figure by the scale factor.

Front

If the scale factor is 2, what happens to the size of the figure?

Back

The figure is enlarged to twice its original size.

Front

If the scale factor is 1/2, what happens to the size of the figure?

Back

The figure is reduced to half its original size.

Front

What is the center of dilation?

Back

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

Front

What is the effect of a negative scale factor in a dilation?

Back

A negative scale factor reflects the figure across the center of dilation and changes its size.

Front

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

Back

To find the image of a point under dilation, multiply the coordinates of the point by the scale factor.

Front

What is the formula for dilating a point (x, y) with center (a, b) and scale factor k?

Back

The image point (x', y') is given by: x' = a + k(x - a), y' = b + k(y - b).