Translations

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

Back

The new point will be (3 + 2, 4 - 3) = (5, 1).

Front

What does the notation (x, y) --> (x, y + 4) indicate?

Back

It indicates a translation that slides the point up by 4 units.

Front

What is the pre-image in a transformation?

Back

The pre-image is the original figure before any transformation is applied.

Front

If a triangle is translated 2 units right and 5 units up, what is the arrow notation for this translation?

Back

The arrow notation is (x, y) --> (x + 2, y + 5).

Front

How do you find the coordinates of a point after a translation?

Back

To find the new coordinates, add the translation values to the original coordinates.

Front

What is the effect of translating a figure 0 units horizontally and 0 units vertically?

Back

The figure remains unchanged; it is effectively the same as not applying any translation.

Front

If Point A is at (1, 2) and is translated to (4, 5), what is the translation vector?

Back

The translation vector is (3, 3), which means moving 3 units right and 3 units up.

Front

What is the difference between a translation and a rotation?

Back

A translation moves a figure without changing its orientation, while a rotation turns a figure around a fixed point.