Translations

Front

What is a translation in geometry?

Back

A translation in geometry is a transformation that moves every point of a figure or a space by the same distance in a given direction.

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (x, y) -> (x + a, y + b), where (a, b) are the horizontal and vertical shifts, respectively.

Front

If a point A is at (2, 3), where will it be after a translation of 3 units right and 4 units down?

Back

A' will be at (5, -1).

Front

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

Back

The shape remains unchanged; it is effectively the same as not translating it at all.

Front

What is the rule for translating a point (x, y) 2 units left and 3 units up?

Back

The rule is (x, y) -> (x - 2, y + 3).

Front

How can you determine the new coordinates of a point after translation?

Back

To determine the new coordinates, add the translation values to the original coordinates: (x + horizontal shift, y + vertical shift).

Front

What is the pre-image in a translation?

Back

The pre-image is the original figure or point before any transformation, such as a translation, is applied.

Front

If a shape is translated 5 units to the left, what is the effect on its x-coordinates?

Back

All x-coordinates of the shape will decrease by 5.

Front

What is the relationship between the image and the pre-image in a translation?

Back

The image is the result of the translation applied to the pre-image; they are congruent but located in different positions.

Front

What does it mean to translate a shape 4 squares down?

Back

It means to move every point of the shape downward by a distance equivalent to 4 units on the coordinate plane.