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 image of a figure?

Back

The image of a figure is the result of a transformation applied to the original figure, known as the pre-image.

Front

If a point (x, y) is translated 3 units left and 2 units up, what is the new point?

Back

The new point is (x - 3, y + 2).

Front

What happens to the point (2, 5) when translated 4 units down?

Back

The new point is (2, 1).

Front

What is the effect of translating a triangle 5 units to the right?

Back

Each vertex of the triangle moves 5 units to the right, changing their x-coordinates.

Front

If triangle A'B'C' is translated to triangle ABC, what does this imply?

Back

It implies that the positions of the vertices of triangle A'B'C' have been shifted to the positions of the vertices of triangle ABC.

Front

What is the translation vector for moving a point 2 units right and 3 units down?

Back

The translation vector is (2, -3).

Front

How do you find the new coordinates after a translation?

Back

Add the translation values to the original coordinates: (x + a, y + b).

Front

What is the difference between pre-image and image?

Back

The pre-image is the original figure before transformation, while the image is the figure after transformation.