Translations and Dilations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you perform a translation on a point (x, y)?

Back

To translate a point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in (x+a, y+b).

Front

What is the effect of translating a point 3 units to the right and 4 units down?

Back

The new coordinates will be (x+3, y-4).

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a center point and a scale factor.

Front

How do you calculate the coordinates of a point after dilation?

Back

To dilate a point (x, y) from the origin with scale factor k, multiply both coordinates by k: (kx, ky).

Front

What happens to the coordinates of point B (4, 9) under a dilation with scale factor k = 2?

Back

The new coordinates will be (8, 18).

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 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

If a triangle is translated 5 units left, what is the transformation rule?

Back

The transformation rule is (x-5, y).

Front

What mathematical operations are used in translations?

Back

Translations use addition and subtraction to adjust the coordinates.