Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by 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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you calculate the scale factor when given original and dilated points?

Back

To calculate the scale factor, divide the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

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

Back

The coordinates of the dilated point are (kx, ky).

Front

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

Back

When a point is dilated with a scale factor of 1, its coordinates remain unchanged.

Front

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

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

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

Back

To find the image of a point (x, y) under dilation with center at the origin, multiply both coordinates by the scale factor k: (kx, ky).

Front

What is the relationship between the original and dilated figures in terms of similarity?

Back

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

Front

If triangle ABC is dilated with a scale factor of 2, what happens to the lengths of its sides?

Back

The lengths of the sides of triangle ABC will be doubled.

Front

How do you determine the coordinates of a dilated point when the center of dilation is not at the origin?

Back

To determine the coordinates of a dilated point when the center is at (h, k), use the formula: (h + k(x - h), k + k(y - k)).