5A: Translations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (x, y) -> (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What does the notation (x + 2, y - 3) indicate?

Back

It indicates a translation 2 units to the right and 3 units down.

Front

If a shape is translated 5 units to the left, what is the mathematical representation?

Back

The representation is (x, y) -> (x - 5, y).

Front

What is the effect of translating a shape 4 units up?

Back

The effect is represented as (x, y) -> (x, y + 4).

Front

How do you determine the new coordinates after a translation?

Back

Add the translation values to the original coordinates. For example, if the original point is (x, y) and translated by (a, b), the new point is (x + a, y + b).

Front

What does the transformation (x, y) -> (x, y - 6) mean?

Back

It means to translate the shape down 6 units.

Front

If a point (3, 2) is translated 3 units right and 2 units up, what are the new coordinates?

Back

The new coordinates are (6, 4).

Front

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

Back

The result is (3, 2).

Front

What does the transformation (x - 4, y + 1) indicate?

Back

It indicates a translation 4 units to the left and 1 unit up.