Dilations and Translations

Front

What is a dilation in geometry?

Back

A transformation that alters the size of a figure, either enlarging or reducing it, while maintaining its shape.

Front

What is the scale factor in a dilation?

Back

The ratio of the size of the image to the size of the original figure.

Front

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

Back

(kx, ky)

Front

What does it mean to translate a figure in geometry?

Back

To move a figure from one position to another without changing its shape, size, or orientation.

Front

How do you perform a translation of a point (x, y) by (a, b)?

Back

The new point will be (x + a, y + b).

Front

What is the result of translating point (3, 4) by (2, -1)?

Back

(5, 3)

Front

What is the difference between dilation and translation?

Back

Dilation changes the size of a figure, while translation moves it without changing its size or shape.

Front

Can a dilation be both an enlargement and a reduction?

Back

Yes, a dilation can either enlarge or reduce a figure depending on the scale factor.

Front

If a triangle is dilated with a scale factor of 2, what happens to its area?

Back

The area is multiplied by the square of the scale factor (2^2 = 4), so the area becomes four times larger.

Front

What is the effect of a scale factor less than 1 in a dilation?

Back

It results in a reduction of the figure.