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 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, b) are the horizontal and vertical shifts, respectively.

Front

What are the effects of translating a point 5 units to the left and 2 units up?

Back

The new coordinates of the point will be (x - 5, y + 2).

Front

If point J is at (0, 1), where will it be after translating 5 units left and 2 units up?

Back

Point J' will be at (-5, 3).

Front

What is the result of a transformation called?

Back

The result of a transformation is called the image.

Front

How do you translate a triangle from one position to another?

Back

To translate a triangle, you apply the same translation vector to each vertex of the triangle.

Front

If triangle A'B'C' is translated to triangle ABC by (x+2, y-9), what does this mean?

Back

It means that each point of triangle A'B'C' is moved 2 units to the right and 9 units down to reach triangle ABC.

Front

What is the translation vector for moving a point from (2, 4) to (7, 1)?

Back

The translation vector is (5, -3), meaning 5 units to the right and 3 units down.

Front

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

Back

Add the translation vector to the original coordinates of the point.

Front

What is the significance of the order of translation in multiple transformations?

Back

The order of translation can affect the final position of the figure if combined with other transformations like rotation or reflection.