Translations

Front

What is a translation in geometry?

Back

A translation in geometry is a transformation that moves every point of a shape 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 translation (x + 3, y - 2) indicate?

Back

This translation indicates that every point of the shape moves 3 units to the right and 2 units down.

Front

If a triangle has vertices at (1, 2), (3, 4), and (5, 6), where will it be after a translation of (x, y) → (x - 2, y + 3)?

Back

The new vertices will be at (-1, 5), (1, 7), and (3, 9).

Front

What is the effect of a translation on the size of a shape?

Back

A translation does not change the size or shape of the figure; it only changes its position.

Front

What is the translation rule for moving a shape 4 units left and 1 unit up?

Back

The translation rule is (x, y) → (x - 4, y + 1).

Front

If point A is at (2, 3) and is translated to (5, 5), what is the translation vector?

Back

The translation vector is (3, 2), meaning it moves 3 units right and 2 units up.

Front

What does it mean to translate a triangle?

Back

To translate a triangle means to slide it to a new position without rotating or flipping it.

Front

How can you determine the new coordinates after a translation?

Back

Add the translation values to the original coordinates: New x = original x + a, New y = original y + b.

Front

What is the result of translating a shape by (0, 0)?

Back

The shape remains unchanged; it does not move.